Taoiseach Enda Kenny has held talks with US President Donald Trump in the White House.
"I love Ireland," said Mr Trump, adding that he would visit the Republic of Ireland during his term in office.
The president told Mr Kenny he was his "new friend" and their governments would forge an even tighter bond.After their meeting on Thursday, Mr Kenny made an impassioned plea for the 50,000 "undocumented" Irish who live in US without legal permission.
"This is what I said to your predecessor on a number of occasions - we would like this to be sorted," he told the president at a lunch event.
"It would remove a burden off so many people that they can stand out in the light and say: 'Now I am free to contribute to America, as I know I can.'"
Noting the presence at the lunch of Northern Ireland politicians Ian Paisley of the DUP and Sinn Féin president Gerry Adams, the taoiseach said: "We want to protect this peace process and I know you are going to work with us in that context also."
Mr Trump quoted from what he said was an Irish proverb that he had heard "many, many years ago".
"Always remember to forget the friends that proved untrue, but never forget to remember those that have stuck by you."
Later, Mr Kenny presented Mr Trump with a bowl of shamrocks for St Patrick's Day.Breakfast
Mr Kenny had breakfast with US Vice President Mike Pence in Washington earlier in the day, in the company of their wives Fionnuala and Karen.
That followed his attendance of the Ireland Funds America gala dinner, which included a speech in which Mr Pence emphasised the commitment of America to the island of Ireland.
He said the US was pledged to securing the gains of the Northern Ireland peace process.
At the dinner, Mr Pence congratulated the people of Northern Ireland for turning out to vote in high numbers during the recent assembly election.
"The advance of peace and prosperity in Northern Ireland is one of the great success stories of the past 20 years," he said.
"We thank those unsung heroes in Northern Ireland who, day-in and day-out, do the difficult and important work - strengthening communities, educating children, building that brighter future for the emerald isle and all who call it home."Mr Pence also recalled his Irish grandfather Richard Michael Cawley, who emigrated to the US from County Sligo in 1923, and spoke with pride about his Irish heritage.
He added that he had thought about his grandfather during inauguration day in January.
"The truth is that whatever honours I will receive over the course of my service as vice president, to receive an honour in the name of the Irish people and my Irish heritage will count as chief among," he said.
"All that I am and all that I will ever be and all the service that I will ever make is owing to my Irish heritage."
Mr Kenny presented Mr Pence with a roll book from a County Sligo school that included the name of his grandfather.
He said Ireland "took special pride in the fact that, for the first time in the history of this great republic, one Irish American has succeeded another in the office of vice president".
The Taoiseach added that immigration was the main focus of his trip to the US.
He said he was pursuing a process where Irish people living in the US illegally can "come in from the cold, and feel the warmth of this great country they have made their home".
A number of politicians from Northern Ireland are in America this week.
Mr Paisley, a DUP MP, who also attended the Ireland Funds America gala dinner, said that he expects little progress to be made during political talks at Stormont until the last minute.
He said he was hopeful the political parties could get "the show back on the road".