And he also ruled out the immediate lifting of the 8pm hospitality curfew, after calls from the industry.
Mr Martin pointed out that Ireland had achieved almost 94pc vaccination rates with an entirely voluntary system - and he said he believed that approach would continue to work into the future for Ireland.
He also pointed out that Ireland had a 63pc booster vaccination rate through an entirely voluntary approach - and this might have exceeded 70pc but for the number of people who had already contracted Covid-19 and had to then wait for their booster jab.
Such vaccination rates were amongst the highest in the world.
"I favour the voluntary - I fully respect that people will explore all issues and research them," he said.
"But from my perspective we have achieved one of the highest rates (of vaccination) in the world through a voluntary system."
"That is the system that we will maintain."
This morning, HSE chief executive Paul Reid said he would prefer to “win people’s hearts and minds” than have mandatory vaccination.
However, he told RTÉ that except for rare medical circumstances he expects all healthcare workers to be vaccinated against Covid-19.
The National Public Health Emergency Team (Nphet) is set to discuss mandatory vaccines in upcoming meetings.
Mr Martin - speaking in Cork - said Ireland will study every aspect of the ongoing battle to control the pandemic.
"First of all I think NPHET will examine every issue - it will give advice to Government from time to time," he said.
"I have been very clear in that I favour the voluntary approach to vaccination. In fact, we have done extraordinarily well as a country - there is a 94pc vaccination rate for the first and second doses.
"There is a 63pc rate for the booster which puts up top of the European league table in terms of the booster campaign.
"I think that speaks volumes for informing the public of the benefits of vaccination and also the robust debate that has taken place with strong medical and public health contributions - not just from officialdom but from those within the academic world, those involved in medicine who have been very, very clear about the benefits of vaccination.
"If you look historically, one of the biggest game-changers in 20th century medicine was the arrival of vaccination whether it was TB, diphtheria, polio, measles - the list goes on.
"Vaccines have had an extraordinary impact on eradicating those diseases."
"Likewise in the context of Covid-19, it is very clear that if you compare this month this year with this month last year - there is no way we would (be this open with our economy).
"We were in Level Five last year - so vaccination is the big game changer here."
Mr Martin also ruled out any immediate easing of the 8pm hospitality curfew but said it was being kept under careful scrutiny.
He also said the latest wave of the pandemic is not expected to peak for at least another week or even fortnight.
"Basically, the European Centre for Disease Control (ECDC) has provided advice to member states across the EU and to public health authorities,” Mr Martin said.
"They are examining that advice and they will be in a position in the next number of days to provide advice to the Government in relation to that issue.
"We understand the pressures that many different sectors (of the economy) are under. I did mention earlier that we need to keep the pressure on the virus and that rule is there - we have to ensure that it does not spread too widely, too quickly.
"I expect that the advice from the ECDC will be interrogated by public health authorities who will (then) advise Government within the next while in terms of any changes that should be made."
Mr Martin said he was particularly conscious of the impact of the 8pm closure rule for the battered Irish hospitality and entertainment sectors.
"We want to give it another week or two. We have not peaked yet (with the latest Covid-19 wave) and the pandemic has had many twists and turns. But I am confident that if we maintain the same focus we can get through this wave,” he said.
"Not this week (8pm closure change) but certainly as I said in relation to close contacts, depending on what advices we receive from the Chief Medical Officer and his team, that’s an issue that has been kept under close review.
The Taoiseach said the Government was carefully monitoring hospitalisation rates with over 1,000 people now within the healthcare system being treated for the effects of the virus.
“If you are hospitalised with Covid-19 it is an illustration of the degree to which Covid can make you sick. We wanted to keep people out of hospital. We certainly also want to keep people out of Intensive Care Unit (ICU) departments,” he said.
“And that has been the rationale for all of our public health policies. In our view case numbers are very very high and we believe that we can manage those case numbers within the existing infrastructure within our hospital and community healthcare system.
“And again I would say to you that is vital that people get vaccinated.
“There are still people out there who could get vaccinated and who haven’t got the booster yet.
“It is very very important that they get the booster - that’s the key measure that people can take to prevent themselves from being hospitalised or being admitted to ICU.”
The Taoiseach said the Government were not assuming the worst of the latest pandemic wave was over.
“The experts are saying to us that it could be a week to two weeks yet before the peak comes,” he said.
“You would’ve heard (HSE boss) Paul Reid saying this morning that certainly with the admissions to hospitals they see no signs of the peak yet and that’s the general view from public health advice.
“And I spoke to the CMO on this recently, and again, he is of the view that it could be a week, it could be two weeks before we see the peak of this yet. So we have to be vigilant. We have to be careful in respect of that.”