Mr Trump has this evening described the Taoiseach as "my new friend, a great guy".
e said Ireland and America could do business under his administration.
In a speech on Capitol Hill Mr Kenny jokingly mocked the President for sticking to his pre-prepared script. Mr Trump is notorious for talking off the cuff during events.
But he said Mr Trump "will have the prayers and support of the Irish people".
The Taoiseach went on to plead with Mr Trump to find a pathway to legalisation for the undocumented Irish.
"We want it sorted," Mr Kenny said.
Earlier as the pair met for the first time at the White House the President confirmed he will visit Ireland during the course of his presidency.
The president said that he "loves" Ireland as he sat in the Oval Office with Taoiseach Enda Kenny.
Mr Trump spoke only briefly while in the presence of journalists to confirm that he "absolutely" intends to visit Ireland.
"I'll be there for sure," Mr Trump said.
Enda Kenny meets with President Trump for the first time (Photo: Gerry Mooney)
Asked whether an invitation had been extended to the president, Mr Kenny said he could come "during the course of his presidency".
A reporter asked whether the president had raised previous comments about Mr Trump's language being "racist and dangerous" but both leaders ignored the question.