Trump made the comments while meeting Taoiseach Micheál Martin at Farmleigh House on Saturday, as the US president continued a busy two-day visit to Ireland.
Speaking about the possibility of Irish unity, Trump said he believed it would happen eventually and suggested that Martin was the person who could help move the issue forward.
The president acknowledged that the UK would inevitably have a role in any discussion surrounding Northern Ireland's constitutional future, but said he believed a united Ireland would be a positive development.
Trump later addressed the subject again at an event at the US ambassador's residence, although on that occasion he offered a more cautious response when asked about Irish unity.
The comments came during Trump's first full day in Ireland, following his arrival at Dublin Airport earlier on Saturday.
He was greeted by Tánaiste Simon Harris and Foreign Affairs Minister Helen McEntee before travelling to Áras an Uachtaráin for a meeting with President Catherine Connolly.
Trump and Connolly held a private meeting at the presidential residence in Phoenix Park. The Irish president has previously been critical of Trump, including over his approach to tariffs, and had faced calls from political parties to raise the issue of Gaza during their meeting.
Trump subsequently travelled to Farmleigh, where he held talks with Taoiseach Micheál Martin.
During the meeting, the US president praised the relationship between Ireland and the United States, describing it as stronger than ever.
Trump said the two countries had a “big relationship” and emphasised the benefits of their close ties. Trade was among the subjects discussed by the two leaders.
His comments on Irish unity are likely to generate particular interest in Northern Ireland. DUP leader Gavin Robinson responded by stressing that the constitutional future of Northern Ireland should be determined by its people rather than politicians elsewhere.
Trump's visit has already prompted a major security operation across Dublin, with authorities preparing for the president's movements between several locations.
The US president is due to continue his engagements in the capital before travelling to Co Clare, where he is expected to attend the Amgen Irish Open at Trump International Doonbeg.
The visit combines political diplomacy with Trump's personal connection to Ireland through his Doonbeg golf resort, but his unexpected remarks on Irish unity have emerged as one of the most significant political moments of his trip so far.
