The President has stood over his decision to decline the invitation to the religious service in Northern Ireland on the grounds that it is political in nature and commemorates the “centenary of the partition of Ireland”.
He also strongly denied any suggestion of a snub on Queen Elizabeth, who is due to attend the service in Co Armagh in October.
Mr Bruton told Newstalk Breakfast the service is a recognition of the existence of Northern Ireland.
"I think he is wrong not to attend, and I think there is time for him to change his mind.
"Obviously it requires great strength of character to change one's mind, but I think he should do so.
"This is not celebrating partition, it is simply recognising a fact.
"And it is important to recognise that fact - the fact that Northern Ireland exists and is legitimate - was recognised by the Irish people when they voted in the referendum on the Good Friday Agreement.
"The Good Friday Agreement accepts that it is the present wish of the people of Northern Ireland that they remain in the United Kingdom until that view is changed.
"So in going to this event and recognising that Northern Ireland existed for the last hundred years, the President would simply be recognising something that the Irish people have recognised."
Mr Bruton says President Higgins' reasoning for not attending, such as his title, does not stand up.
"No, they don't provide an explanation.
"This was one of the most important invitations he would have received as President - it wasn't an invitation to the opening of a credit union in Co Kerry.
"This was an invitation to attend an event which deals with a very difficult issue upon which policy is made by the Government.
"We can't have two policies on Northern Ireland - one being made by the Government is Merrion Street, and another being made in the Phoenix Park.
"There can only be one policy of the State is regard to how to deal with the problems of Northern Ireland.
"Reach out to the unionist community, which we need to do, both over the Northern Ireland Protocol and also over the future of our country".
Speaking in Rome during a four-day official visit to the Italian capital, President Higgins said his problem was with the title of the event, which it was stated would “mark the centenaries of the partition of Ireland and the formation of Northern Ireland”.
He said the title was politicised and made it inappropriate for him as head of State to attend the event.
“What [had started out as] an invitation to a religious service had in fact become a political statement,” he said. “I was also referred to as the President of the Republic of Ireland. I am the President of Ireland.”
In a reference to Queen Elizabeth, he said: “There is no question of any snub intended to anybody. I am not snubbing anyone and I am not part of anyone’s boycott of any other events in Northern Ireland.
“I wish their service well but they understand that I have the right to exercise a discretion as to what I think is appropriate for my attendance.”
In response to DUP politicians who claimed he had snubbed the event, he replied: “It’s a bit much, to be frank with you. I have gone up to Northern Ireland to take part in events.”
“There often has not been a great deal of traffic down from the DUP people who are criticising me now,” he added.