Mr Martin said he will be meeting President Michael D Higgins as part of normal Constitutional and Government procedures next month - but refused to say if the letter controversy will be brought up.
He confirmed that he had not to date spoken with Mr Higgins about the issue.
The Fianna Fáil leader also refused to say whether he would ask for a review of the practice whereby the spouse of the serving President has the capacity to have personal material published on the official President’s website.
"I think we need to have a sense of perspective. There has been a lot of debate - that is important - we live in a democracy and it is good that we have people's viewpoints articulated," he said.
"From all involved, my view is that it is time to move on from it now.
"The key point is that the Irish Government position is rock solid on what should be done here - Russia needs to withdraw at a minimum back to the positions when the war started.
"There is no excuse for the type of war crimes that Russia has committed. The level of violence it has inflicted on the Ukrainian people. It strikes at the heart of the multi-lateral world order."
Mr Martin said Mrs Higgins explained the letter was written in a personal capacity - and the President had also clarified the position.
"The President himself issued a statement, through his spokesperson, and gave his longstanding articulation of his condemnation of the Russian invasion of Ukraine.
"I think Sabina Higgins has clarified the situation in terms of her statement," he said.
"The President, to be fair, has also reiterated his strong condemnation of the Russian invasion of Ukraine.
"The Irish Government's position has been consistent from the outset and it remains the position that the invasion was both illegal and immoral.
"It was a terrible act against the people of Ukraine.
"We live in a democracy and we are conscious of that and people are entitled to their viewpoints.
"We are all agreed on the need for peace. There is no argument there.
"The Government's view is that Russia has to stop the violence and stop the war and withdraw from the territory of Ukraine."
Mr Martin refused to be drawn on whether lessons needed to be learned from the controversy and the use and oversight of the President’s website.
"Sabina Higgins has clarified her position. I don't see it that way (that political parties were embarrassed). From the Government point out view, I don't think anyone is in any doubt about the Irish Government's position on the war in Ukraine.
"I don't think the Ukrainian Government is (confused about Irish support).
"I have spoken with President Zelensky so I think we have to keep everything in perspective.
"Clarity has come from the President, clarity has come from Sabina Higgins herself. Everybody accepts there is no equivalence between Vladimir Putin and President Zelensky.
"Ukraine did not want this war, Europe did not want this war and Europe tried everything it could, with President Biden, to prevent this war from occurring.
"Terrible, terrible damage has been done as a result of the war and terrible loss of life has occurred.
"It is needless, it is reprehensible and it should end."
Mr Martin declined to say if the capacity for the spouse of the President to publish material on the official Presidential website might now be reviewed.
"I think the explanation is that it is not the first time...we do know that the spouse of the President, a practice has built up over the years where they may go to a particular opening or adopt a particular cause for the benefit of the community.
"That has been happening for quite some time. I think we need to understand that an informal practice has built up over the years.
"What is clear is that the Government position has not changed nor do I believe that, in terms of the Ukrainian Government or people generally, I think they are well aware of our position as articulated on a consistent basis at the UN Security Council."
The Taoiseach said he had seen for himself the war crimes committed in Ukraine.
"I visited Ukraine myself and went to Bucha and Irpin where I saw at first hand - I met families who were very affected by the terror of the war and by the crimes that were committed in terms of the targeting of innocent civilians.
"The towns I visited were not military installations.
"Our position along with others in the EU is unequivocal - that Russia should withdraw to, at a minimum, the positions it had before the war started.
"In our view, we are clear that many efforts were made by many EU leaders including Chancellor Scholtz, President Macron to get Russian President Vladimir Putin - to deter him from starting the war in the first instance.
"Unfortunately, I think he (Putin) has an imperialist 19th century view of life.
"He resolved to invade Ukraine and he did."