US president Donald Trump described Taoiseach Enda Kenny as his “new friend” and a “great guy” as the two attended the annual Speaker’s Lunch in the US Capitol to mark St Patrick’s Day.

Mr Trump said the bond between Ireland and the US during his presidency is “going to be closer than ever before”.

“The people of Ireland and the people of the United States have stuck together through good times and bad times,” he said. “Over many centuries we have built a bond that thrives, inspires and endures. And with us, it’s going to be closer than ever before, I can tell you that.”

Mr Trump said that Irish immigrants and their descendents had made “tremendous contributions” to American life, recalling past St Patrick’s Day parades in New York.

US president Donald Trump walks away after shaking hands with Taoiseach Enda Kenny, Ireland’s prime minister, right, following a Friends of Ireland lunch with US House speaker Paul Ryan (left) in Washington D.C. on Thursday. Photograph: Andrew Harrer/Bloomberg.

Among the attendees at the annual speaker’s lunch were Sinn Féin leader Gerry Adams, DUP politician Ian Paisley Jnr, and Mr Trump’s adviser Kellyanne Conway.

Invitation

Earlier, Mr Kenny confirmed he had invited Mr Trump to visit Ireland during his presidency, because in Ireland “invitations are always returned, and returned in kind.”

Mr Kenny also congratulated Mr Trump on his electoral victory. “You beat them all, whatever they say,” he said, noting that he had contested 20 general elections himself.

The fountain on the south side of the White House is dyed green for St Patrick’s Day in Washington DC, US. Photograph: Olivier Douliery/EPA

The Taoiseach also said he held a very “constructive, beneficial” discussion with Mr Trump on immigration issues.

Mr Kenny said he had raised both the issue of legal immigration paths for Irish people, including the revival of a stalled proposal of a new E3 visa scheme, as well as the situation of undocumented Irish citizens living in the United States.

He said the president had been surprised at the number of undocumented Irish living in the country - said to be 50,000 - and had expected it to be much higher.

Undocumented

Mr Kenny said Mr Trump told him that his primary focus in terms of immigration was on border security, secondly on those who had criminal records, and then on anyone else who might be undocumented.

“I would say to Irish documented, if there are small issues like parking fines, or traffic lights, they should clear those up through their legal people...That’s an issue that can lift the concern and the fear and anxiety that many undocumented Irish might have. At the end of the day, this is going to require cooperation on the Hill between Republicans and Democrats.”

The Taoiseach also met the head of the Homeland Security, John Kelly, who has been at the forefront of implementing Mr Trump’s controversial clamp-down on immigration.

US president Donald Trump meets Taoiseach Enda Kenny in the Oval Office of the White House. Photograph: Kevin Lamarque/Reuters.

Mr Kenny also raised the issue during his speech to members of Congress at the annual Speaker’s Lunch.

“On this day when we remember St Patrick, himself an immigrant twice over to our shores, I urge you to look sympathetically at this issue,” he said, noting that many of them came to the US “decades ago, in a different era, and have been caught in limbo without any path to regularise their status.”

Mr Kenny will later return to the White House for the annual presentation of a bowl of shamrock to the president.