Taoiseach Brian Cowen and US President Barack Obama met for over half an hour in the Oval Office today.
Before the traditional shamrock ceremony, President Obama spoke about his Irish roots.
He said at some stage in the future he would like to visit Ireland.
The Taoiseach spoke about the strength of the relationship between Ireland and the US.
At one point, President Obama jokingly suggested that he and Brian Cowen might be cousins.
The Taoiseach responded that he would not like Mr Obama to run against him in Offaly- the President’s ancestral home - because the US leader would beat him.
Later, the two leaders took part in the traditional St Patrick's Day Shamrock Ceremony, which symbolises the friendship between the two countries.
This is Mr Cowen's first visit to the White House as Taoiseach.
The 40 minute bi-lateral meeting in the Oval Office is only the third which President Obama has held with a foreign leader since taking up office in January.
Yesterday, the Taoiseach was guest of honour at the Annual American Ireland Fund Dinner in Washington.
In his address the Taoiseach referred to the recent killings in Northern Ireland.
He said that a tiny evil minority sought to destroy what the people have Ireland have built, but he said they will not succeed.
Tonight President Obama and his wife Michelle will host a St Patrick's Day reception as the White House.
Meanwhile, Northern Ireland's first and deputy first ministers will also meet with President Obama during the celebrations.
Peter Robinson and Martin McGuinness twice delayed their departure for the US because of last week's murder of two British soldiers and a policeman.
During their visit, the leaders have been promoting business opportunities in Northern Ireland.