A small section of the crowd - many displaying Republican flags and banners - repeatedly jeered both Mr Martin and Mr Varadkar as they spoke
Both said his legacy is the proud, outward-looking and successful modern republic that Ireland has become.
The Taoiseach and Tanaiste both spoke at the Béal na mBlath commemoration in west Cork with over 10,000 people in attendance.
However, a small section of the crowd - many displaying Republican flags and banners - repeatedly jeered both Mr Martin and Mr Varadkar as they spoke.
The small group of hecklers were immediately drowned out by the majority of the crowd who applauded the speakers and shouted for respect.
In a moment of drama, Mr Martin had to pause his oration as a member of the Defence Forces honour guard on duty behind him collapsed onto the concrete.
The soldier - who is believed to have suffered heat exhaustion - was immediately carried away for medical treatment.
He recovered and later met the Taoiseach who checked on his welfare.
The Taoiseach hailed General Collins as "one of the great heroes of Irish history."
But Mr Martin also hit out at those "who have tried to abuse the memory of that (independence) struggle."
"Critical for our country is that we have avoided the extremes of the left and the right which brought such misery to other countries in the last century," the Taoiseach warned.
"The centrist, democratic politics which emerged in our country has achieved far more than any other approach could possibly have achieved."
"We need to do more to confront the new revisionism of those who try to denigrate our country's achievements, and who try to claim legitimacy for violent campaigns waged in the face of the opposition of the Irish people."
Mr Martin later clarified he was referring to the Provisional IRA who waged a 30 year campaign of violence despite the opposition of the overwhelming majority of the Irish people.
"We have to give no quarter to their attempts to link themselves to the men and women who fought our revolution over a century ago."
Mr Martin also hit out at what he called "a lazy tendency to dismiss Irish politics as so-called civil war politics."
He said the willingness to try to find common ground was one of the great strengths of modern Ireland.
Over 10,000 people gathered at Béal na Bláth in west Cork to mark the anniversary of the death of the Free State finance minister and IRA intelligence director at the height of the bitter Civil War.
General Collins - fondly known as the 'Big Fella' - was shot and killed during an inspection tour of his native Cork on August 22 1922.
The ceremony was told it was "the shot that was heard around the world."
Aged just 31 years, General Collins was the only casualty of an ambush staged by a small anti-Treaty group in an isolated west Cork valley known as the 'mouth of the flowers.'
General Collins was the driving force behind the establishment of the Free State and had masterminded the guerilla warfare tactics that had fought Crown forces to a standstill during the War of Independence.
The Woodfield native had insisted, after being warned about the dangers posed by the tour of inspection in August 1922, that he wouldn't be shot in his native Cork.
The centenary ceremony featured full military honours, the presence of the Sliabh na mBan armoured car that accompanied General Collins on that fateful day and a memorial site lavishly refurbished by Cork Co Council.
As well as the Taoiseach and Tánaiste, the ceremony featured Foreign Affairs Minister Simon Coveney, Justice Minister Helen McEntee, Finance Minister Paschal Donohoe, Higher Education Minister Simon Harris, Defence Forces chief of staff Lt Gen Sean Clancy, Mayor of Cork County, Councillor Danny Collins, and the Lord Mayor of Cork, Councillor Deirdre Forde.
Former European Parliament President Mairead McGuinness was also in attendance.
Extended members of the Collins family were also present.
General Collins' grandniece, Eleanor Moore, paid tribute to the Taoiseach, Tánaiste and organising committee for the elaborate centenary ceremony.
Ms Moore is the great-granddaughter of General Collins' sister, Mary.
"I am both honoured and humbled to be representing the extended Michael Collins family on this the centenary anniversary of his death," she said.
"It has been an amazing weekend for the family as we have met and chatted to many followers of Michael Collins and his legacy."
She cited a newspaper report of August 24 1922 on the legacy of General Collins.
“In every phase of the awakened activity of the nation-constructive, administrative, executive, military – the personality of Michael Collins was vivid and impelling. He has been slain to our unutterable grief and loss – but he cannot die. He will live in the rule of the people, which he gave his great best to assert and confirm, and which his colleagues undertake as a solemn charge to maintain."
She also recalled her great-grandmother's moving tribute to her lost brother.
"In 1923 the Irish National Army commissioned and erected the beautiful and impressive memorial cross and monument at this place as a mark of respect and to honour the memory of their first commander in chief. For me as a relative, there was also the personal aspect. My great grandmother Mary Collins laid a wreath with the simple inscription: 'To Michael from Mary'."
The Taoiseach in his oration said Ireland had moved on from old Civil War divisions - and the modern nation appreciated the values and principles that General Collins had fought and died for.
He said it was "an honour and a privilege" to have been asked to deliver an oration at Béal na Bláth.
"He (General Collins) is today, as much as he has ever been, an inspiring symbol of how much we can achieve in the face of even the most terrible odds."
"When we look back over what has been achieved in the last century I have no doubt that Collins would see a country transformed - an Irish state which has proved to the world that it can achieve great things when it is free to shape its own destiny."
The Taoiseach hit out at those cynics who claimed little had been achieved in 100 years and that Ireland was close to being "a failed state."
He said Ireland went from one of the poorest countries in the world in 1922 to one of the most developed.
The population has grown by two million and Ireland now boasts one of the highest and most sustained increases in life expectancy worldwide.
While the country does face challenges, he warned that its achievements such not be denigrated.
The Taoiseach noted that General Collins "was never into hero worship and he always saw himself as part of a broad movement."
During the fractious Treaty debates and the ensuing Civil War, he never resorted to personal attacks.
"He did not demonise others because he remembered all he had gone through with them as colleagues and friends," he said.
"He never celebrated deaths of opponents and showed deep compassion - openly weeping when he heard the deaths of former colleagues like Cathal Brugha."
Mr Martin said that when news of General Collins death spread, Republican prisoners greeted it with sombre silence and prayers.
"It is perhaps the greatest tragedy of Collins' death that it deprived us of our best hope for reconciliation.
"The bitterness which grew out of the events of the following year showed how much was lost in this place."
The Taoiseach said modern Irish politicians must also remember how General Collins worked relentlessly to try to protect Northern nationalists.
"Collins acutely felt the outrage of creating a state based on a sectarian headcount - but he also didn't believe that a new Ireland could be built through a deadly conflict between the two major traditions which share our island."
"For too long people ignored that fact. That remains our challenge - to do the hard work of moving words to real action on building a shared island, an island where we show respect for our past but we embrace the much harder work of reaching out and respecting each other."
"This commemoration is an important statement of remembrance and gratitude. It is a mark of our respect for one of the great heroes of Irish history, a man who played an irreplaceable role in securing Irish freedom."
He said that while Béal na Blath was special to the Fine Gael tradition, "it is also an important site for all who honour and respect our independence struggle and our democracy."
He noted that then Taoiseach Jack Lynch had designated the Collins homestead as a national monument, that then Defence Minister Jerry Cronin had laid a wreath at the commemoration and then Finance Minister Brian Lenihan had delivered the oration in 2010.
"These and many other generous and open gestures have helped ensure that democratic Irish nationalism has found so much common ground in looking back at our history and the role of our founders in winning independence."
Tánaiste Leo Varadkar said that, for many, Béal na Bláth was "a painful site of memory...it is a place of death forever associated with a senseless killing in an unnecessary war which turned brother on brother."
But he stressed it was also a place where the legacy of General Collins shone brightly and where Irish citizens 100 years on remember the principles he gave his life for.
"These are the foundation stones of our State: the right of all nations to self-determination; democracy and the democratic institutions; freedom both personal and political; the rule of law; respect for others; and the unshakeable belief that Ireland can be ‘a shining light’ onto the world."
"Civil wars, by their nature, leave a bitterness which it can take a very long time to heal, whether in Ireland, Spain, the United States or Greece. Undoubtedly the Irish Civil War was such a conflict and left a painful legacy which stunted our development in the years that followed."
He paid tribute to the efforts to end old Civil War divides - and singled out the late Fianna Fáil minister Brian Lenihan for praise.
Mr Lenihan, who was battling cancer in 2010, became the first Fianna Fáil minister to ever speak at Béal na Bláth.
"In becoming the first Fianna Fáil minister to speak here, he knew that he was performing 'a public act of historical reconciliation,' to use his words.
"It was an act of courage, typical of the man. As we all know it was a terrible time in his life as he did everything he could to try to save the economy while at the same time receiving treatment for the cancer that was to end his life only ten months later."
"His words in 2010 still resonate today - 'The spirit of Collins is the spirit of the nation.' It must continue to inspire everyone in public life, irrespective of party or tradition."
Mr Varadkar also paid tribute to the Taoiseach for accepting the invitation to deliver the joint Béal na Bláth oration.
The Fine Gael leader said that, today, Ireland appreciated the true legacy of General Collins.
"He was both an idealist and a realist. As he predicted, the Treaty gave us freedom and the freedom to achieve more freedom in the future. Others fought on for decades, only to accept Collins’ approach almost a hundred years later."
"Unlike others, whose defining idea was the achievement of the Republic, who found themselves unable to compromise to bring it into existence, Collins viewed freedom in a different way."
"He saw it as something that was more than simply a description. To have real meaning, it had to be felt and experienced and lived."
"Michael Collins never intended his legacy to be the last word on Irish freedom. Instead, he gave us the freedom to find our own path to it.
"On the centenary of his death, we pay tribute on behalf of a grateful nation and join together to say, ‘Thank you’. Michael Collins’ life was Ireland. His legacy is Ireland too."