Trump made the remarks during a meeting at Farmleigh House as part of his two-day visit to Ireland.
Asked about Irish unity, the US president said he believed it would eventually happen and suggested that Mr Martin could play a role in advancing the issue.
Trump acknowledged that the British government would have a say in the matter, but said he could see no reason why Irish unity would be negative.
His comments are likely to attract considerable attention in Northern Ireland, where the constitutional question remains a politically sensitive issue.
DUP leader Gavin Robinson rejected Trump's intervention, arguing that Northern Ireland's constitutional position should be determined by its own electorate.
Mr Robinson said the future status of Northern Ireland would not be decided by political figures or commentators in London, Dublin or Washington, but by the people of Northern Ireland.
The president's comments came during a packed schedule in the Republic, which began with his arrival at Dublin Airport before he met President Catherine Connolly at Áras an Uachtaráin.
Trump and President Connolly held a private meeting at the presidential residence in Phoenix Park. Connolly has previously been critical of the US president and has been outspoken on the situation in Gaza.
Political parties including Sinn Féin had urged the president to raise the issue of Gaza with Trump during their meeting.
Later, while speaking at an event at the US ambassador's residence, Trump appeared more guarded when asked again about Irish unity.
He suggested that there was no straightforward response to the question before indicating that his earlier comments would be widely reported.
The US president also used his meeting with Mr Martin to praise the current state of relations between Ireland and the United States.
Trump described the relationship as particularly strong and said the two countries were working well together.
Trade was among the issues discussed during the meeting.
Trump's visit comes after months of preparations and one of the largest security operations undertaken for a visiting political leader in the history of the Irish state.
The president is due to continue his Irish itinerary before travelling to Co Clare to attend the Amgen Irish Open at Trump International Doonbeg.
