Events are taking place in Dublin to mark the centenary of the 1916 rebellion against British rule, a seminal moment in Ireland's past.
Some unionists have been reluctant to take part in or support the events.
Michael D Higgins also said the commemorations are an example to the UK of how to reflect on its own history.
The Easter Rising, a brief and militarily unsuccessful republican revolt, is seen by many historians as a significant stepping-stone in the eventual creation of the Republic of Ireland and the partition of the island.
A greater depth of knowledge, President Higgins said, meant the Easter Rising was now being put "in context of what was happening in Europe" 100 years ago.
"I do think that without 1916, and the events that surrounded it, we would not have achieved our independence," he said in a wide-ranging interview for the BBC.
"It is one of the founding events, without a doubt, and it is of immense significance in terms of where it occurs historically but also symbolically."
President Higgins said Ireland's approach to the rising's centenary was one of "ethical sensitivity".
And he added that "it is responsible not to be seeing fears where there are none".
"My great hope, as head of state, is that we will put ourselves into each other's history," he said.
"We must be able to take your version, my version, move into the shoes of the other, and we must be open to changing our versions as new facts, information and analysis become available to us.
"I would hope that people in Northern Ireland will approach these commemorations, and as we commemorate the [Battle of the] Somme, that we'd be able to do so generously."
President Higgins said people must not "become a prisoner of the past" and "mustn't allow any distortions of history".
He said everyone's take on history must be open to critique, and that Britain, like Ireland, had to closely examine its past.
"When we decide to address the issue of violence, let us speak of the violence of empire, the violence of state, the violence of insurrection," he said.
"Let's do it all - this is the challenge that people are not rising to.
"Having spent decades revising nationalism, where is the evidence that there is as much energy put into addressing the issue of empire?
"As empires came to establishing their stamp on neighbouring countries, what was the consequences of that?"
He described the Northern Ireland peace process as "fragile" and an "ongoing project", but added it would be "pessimistic and wrong" to say significant reconciliation had not been achieved.
"There is real reconciliation going on," he said.
"You don't keep picking at the sources of division to undermine what progress you're making in the present in terms of reconciliation."
Earlier this week, the Inniskillings Museum in Enniskillen, County Fermanagh, presented President Higgins with a green harp flag that had been taken by a soldier from Dublin's Liberty Hall during the rising.
The Irish president has said he hopes people in Northern Ireland will approach the Easter Rising commemorations "generously".