The Taoiseach and the US President are meeting at the moment as part of the annual St Patrick's Day celebrations.
They exchanged the traditional bowl of shamrock in a virtual event held in the last hour.
President Biden spoke about his Irish roots and deepening the connection between the two countries.
Mr Biden also expressed “strong support” for the Belfast agreement.
He told the Taoiseach that he hopes the traditional St Patrick's Day visit can take place in the White House next year.
He also spoke about the shamrock tradition.
“It’s a great tradition, a custom that goes all the way back to Harry Truman . . . tonight, Taoiseach, I hope you will be able to see it remotely, we’re going to light up the White House in green to celebrate the deep, deep affection that we Americans have for Ireland and the people of Ireland,” he said.
“It includes millions of Americans like my great-great grandfather, my great grandfather and my grandfather, all of whom were Irish Americans, on both sides of the family.”
Earlier, Mr Martin met vice-president Kamala Harris who said the relationship between the US and Ireland remains strong.
“Happy St Patrick’s Day on behalf of our country. As you know, our country has a long history, of friendship, of shared values and culture,” she said.
She said she looked forward to hosting the Taoiseach in person next year.
“On behalf of the president I would like to thank Ireland for advancing our shared values as a member of the United Nations Security Council and also thank you for our robust economic partnership,” she said.
“We take great pride in what we have created around technology. And we have great admiration for the work you’re doing in Ireland and the partnership we share.”
Earlier on Wednesday, Mr Martin held a virtual meeting with House Speaker Nancy Pelosi where the Belfast Agreement, immigration and efforts to secure access for Irish people to the E3 visa were discussed.
