The Taoiseach has said he wants to "do a deal" with President Donald Trump on a solution for Ireland's "undocumented" citizens living in the US.
Leo Varadkar stressed the need for certainty for the tens of thousands of Irish who reside illegally in the United States - "living in the shadows" with the threat of deportation hanging over them.
Mr Varadkar used the traditional Shamrock presentation in the White House to offer Mr Trump a reciprocal resolution, though he stopped short of publicly outlining what Ireland would offer in return.
"I want to assure you, Mr President, that the Irish Government will continue to work with your administration to find a solution to this important issue," he said in a speech in the East Room of the White House.
"And we are ready to do a deal."
The shamrock presentation marked the last joint engagement for the two leaders in the traditionally packed schedule of St Patrick's events in the US capital.
Earlier in the day, the two men discussed the undocumented issue in the Oval Office. Mr Varadkar emerged to say the president was keen to find a solution.
"It was something that was very much on his mind," he said.
"We have a measure of support and degree of enthusiasm from the administration to work on a solution for thousands of Irish people who are here undocumented but who are hard-working, tax-paying people who are very loyal to America."
Earlier Mr Trump pledged to visit Ireland and said he would go to the border.
Ahead of the formal meeting with Mr Varadkar in the Oval Office, the president said the trip could happen next year.
Mr Trump was asked by reporters if he would like to visit Ireland soon.
He said: "I will. I love it, I love it.
"I have property there and I might not get to see it again, but I will."
The Taoiseach said a firm date for his visit to Ireland had not yet been set - but the president had a "standing invitation".
President Trump owns a golf course at Doonbeg in Co Clare.
The same golf course would later prove the source of controversy.
Varadkar faced criticism from political rivals back in Ireland after recounting an anecdote that he had phoned authorities in Co Clare four years ago to inquire about a planning application for a windfarm near a golf course owned by Mr Trump.
During Speaker Paul Ryan's traditional St Patrick's lunch on Capitol Hill, Mr Varadkar recalled how Mr Trump has called him at the time to highlight his concern about the windfarm plan.
With the windfarm application having been subsequently turned down, opposition parties have now demanded to know the extent of Mr Varadkar's intervention.
A spokesman for the Taoiseach later insisted he had not acted inappropriately.
After the Oval Office meeting, which also involved vice president Mike Pence, the Taoiseach confirmed the potential impact of Brexit on the border was discussed.
"The president was very aware of the issues that could affect Northern Ireland if there is a return to a hard border and I think will be very much on our side in working for a solution to make sure that doesn't happen," he said.
Earlier Mr Trump had described the border as "interesting".
"That is an interesting border also, we have two interesting borders", he said, apparently alluding to the US/Mexico frontier where he wants to build a wall.
Trade was also discussed in the Oval Office bilateral.
"The president has enormous concerns that the United States isn't being treated fairly when it comes to trade by China and by Europe," said the Taoiseach afterwards.
"I put across the view that maybe the best way to resolve that is for a new deal, a new trade deal between America and Europe, and the president seemed very open to that."
Reporters also asked Mr Varadkar about Mr Pence's decision not to allow the media to attend their scheduled meeting at his residence on Friday morning.
The Taoiseach has pledged to raise issues around the vice president's controversial stance on LGBT rights.
Mr Varadkar said he would have preferred if the cameras were allowed in to document their comments, but he added: "It allows us maybe to have a frank conversation that's easier to have without the media present."