The US president also cast doubt on Britain’s ability to defend the Falkland Islands during the visit to Ireland.
Donald Trump triggered a diplomatic row as he backed a united Ireland on a visit to Dublin on Saturday.
Speaking to reporters, the US president claimed Irish reunification as inevitable, adding it “may as well happen now”.
His comments brought a stern rebuke from the Conservatives in the UK while Downing Street pointed to Andy Burnham’s rejection of an immediate border poll earlier in the week.
Answering a question from the Press Association, Mr Trump said: “I’d love to see it unified. I think it would be a great feather in everybody’s cap if that happened. It’s going to happen eventually.”
Referencing Taoiseach Micheál Martin sitting next to him, Mr Trump added: “We’re talking about it and you got the right man over here to get it moving.
“But, yeah, I think it would be a fantastic thing.
“Now the UK will have something to say about it, obviously. But I think it would be a great thing. I mean, how can it be bad?”
The comments are likely to further strain relations between the US and the UK, with Mr Trump also casting doubt on Britain’s ability to defend the Falkland Islands during the visit.
On Wednesday, Mr Burnham told MPs a border poll would only be considered when there was “a clear consensus in the country”.
Conservative deputy leader Alex Burghart said Mr Trump was “very wrong”, adding Northern Ireland was “an integral part” of the UK.
The row could also complicate Washington’s relations with Northern Irish parties.
While Sinn Féin has boycotted the annual St Patrick’s Day visit to Washington over Mr Trump’s Middle East policy, leading unionist parties the DUP and UUP have continued to engage with the president.
In response to his comments, DUP leader Gavin Robinson said Northern Ireland’s future would be decided by its people, not “commentary in London, Dublin or Washington”.
He added: “As unionists, we are not interested in the destruction of our country by joining with the Irish Republic.”
Traditional Unionist Voice leader Jim Allister said Mr Trump was “not the first US president to meddle in the affairs which don’t concern him”, adding: “Northern Ireland is not a pawn in Trump’s fallout with the UK.”
Sinn Féin leader Mary Lou McDonald said the president’s comments were “timely” and Mr Martin “must now begin planning for a united Ireland”.
The UK-Ireland border remains a sensitive issue, with Mr Burnham triggering a political row earlier in the year after saying a referendum on reunification was “off the table”.
Under the terms of the 1998 Belfast/Good Friday Agreement, the UK’s Northern Ireland secretary can decide to hold a border poll, and has a duty to call one if it appears likely a majority would vote for Irish unification.
The people of the Republic of Ireland must also vote in favour to effect constitutional change.
Mr Trump’s comments came at the start of a two-day visit to Ireland, during which he will meet political figures and watch the Irish Open golf tournament at his resort in Doonbeg, Co Clare.
On Saturday morning, he met with Irish President Catherine Connolly at Áras an Uachtaráin in Dublin’s Phoenix Park before meeting Mr Martin at Farmleigh House.
Mr Trump said America’s relationship with Ireland had “never been as good as it is right now” while Mr Martin praised the “sporting relationship” between their two countries.
The visit has also seen significant protests on the streets of Dublin, sparking what has been described as one of the biggest security operations ever implemented by the Irish police service (An Garda Síochána).
Garda Commissioner Justin Kelly said peaceful protest would be facilitated as much as possible, but there would be “no tolerance” for public disorder or attempts to impact “critical movements” of the US president.
In her own meeting with Mr Trump, Ms Connolly said she had “conveyed the strong view of the Irish people that the normalisation of war and genocide can never be accepted”.
Last year, the Irish president had accused her US counterpart of being “volatile” and “acting like a bully”.
