Donald Trump has said he would “love” to see a united Ireland and that it “may as well happen now”.

The US president appeared to endorse the push for constitutional change on the island at the start of a two-day visit to Ireland on Saturday. The unexpected intervention prompted a swift rebuttal from the UK government and Northern Ireland’s unionist leaders.

“I don’t want ⁠to cause any problems, ​but ‌I will ‌tell you, I’d love ‌to see it unified,” Trump told reporters at joint press conference with the taoiseach, Micheál Martin, in Dublin. “I think it would be a great feather in everybody’s cap if that happened. You know what? The way I look at it, it’s going to happen eventually. It may as well happen now.”

The unification of Northern Ireland with the republic of Ireland would be “fantastic”, Trump said. “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 intervention jolted his hosts and came two weeks after Andy Burnham said a referendum on unification was “off the table”, which angered Sinn Féin and other Irish nationalists.

Speaking later on Saturday, Trump acknowledged that his comments on unification, made in response to a reporter’s question, would be controversial. “No matter what you say or how you say it, there’s no good answer,” he said. “I gave a nice answer, I think. We’ll worry about it tomorrow.” Unification, he added, would be a “very cool thing”.

A Downing Street spokesperson said the prime minister still believed there was not the required support for unification to trigger a referendum, as set out in the Good Friday agreement.

Gavin Robinson, the Democratic Unionist party (DUP) leader, said Northern Ireland’s constitutional future would be decided by its people, not by commentary in London, Dublin or Washington.

“Northern Ireland is part of the United Kingdom because that is the settled democratic will of its people. I am confident Northern Ireland will continue to choose the UK and the security it offers. As unionists we are not interested in the destruction of our country by joining with the Irish republic.”

Colum Eastwood, an MP and former leader of the Social Democratic and Labour party (SDLP), and frequent critic of Trump, posted a clip of the president’s remarks on social media and wrote: “Always liked him.”

The Conservative leader, Kemi Badenoch, said: “President Trump is shooting from the hip as usual, just like he did with Greenland and Canada becoming the 51st state. This sort of loose talk about the future of democratic countries is deeply unhelpful and creates unnecessary tension.”

Trump’s comments strayed from predecessors who sought to keep the White House neutral on Ireland’s constitutional future, but the off-the-cuff nature of the remarks suggested there was no change in US policy.

Trump’s unofficial visit is centred on golf – he flew on Saturday afternoon to his resort in Doonbeg, County Clare, which is hosting the Irish Open – but started with a courtesy call in Dublin to Áras an Uachtaráin, the official residence and workplace of the Irish president, Catherine Connolly.

Before her election to the ceremonial post last year, Connolly called Trump a bully and criticised his policies in Gaza and Iran. Their brief encounter, behind closed doors, appeared to go smoothly despite a coded critique of White House policies.

Connolly said in a statement afterwards that she “conveyed the strong view of the Irish people that the normalisation of war and genocide can never be accepted” and stressed the importance of the United Nations – an organisation Trump has disparaged. Trump said they had a wide-ranging discussion, including about energy and water, and that Connolly was “terrific”.

Trump held a separate meeting with Martin at the Phoenix Park, where he told the press that Iran would seek peace after the US midterm elections and repeated his claim that his war had prevented Tehran obtaining a nuclear weapon.

Asked about protests against his visit – a large crowd was expected in central Dublin, 5 miles away, as well as at Doonbeg – the president said he had not seen any protests.

Addressing guests as at the US ambassador’s residence, Trump assailed US Democrats as extremists and criticised Europe’s approach to immigration.

He lauded US-Irish relations but reiterated a complaint about the American pharma giants in Ireland. “You took all our medical companies, we’ve got to get a couple of them back. You fleeced us but that’s OK. There’s a lot of room to go around and our relationship with you is fantastic.”

As he left Dublin a crowd at the Garden of Remembrance waved banners and chanted: “Donald Trump, can you hear? We don’t want you here.”

Trump is expected to stay overnight in Doonbeg and present the Irish Open trophy before returning to Washington on Sunday.