Ireland will find the United States to be "an ever faithful partner and a loyal friend" under Donald Trump's leadership.
The president told the 'Shamrock Ceremony' that Irish Americans "played a vital role in protecting our union in the hour of its greatest need".
He said they had earned the nickname of the "fighting Irish".
Taoiseach Enda Kenny told Mr Trump that he held the "future of America, and indeed the world" in his hands. After handing over the traditional bowl of shamrock, he said the US President was taking up a job that was "exceptionally demanding and difficult".
"The United States remains the most influential, as well as, the most powerful country in the world."
Speaking at a party in the East Room of the White House, he thanked Mr Trump for "giving so much of his time" to help celebrate St Patrick's legacy as "the patron of immigrants".
He appealed to the President to take a more favourable view of immigrants - but made no mention of Mr Trump's controversial travel ban on six predominantly Muslim countries.
"Ireland came to America, because deprived of liberty, opportunity, safety and even food itself, we believed.
"Four decades before Lady Liberty lifted her lamp, we were the wretched refuse on the teeming shore," Mr Kenny said.
"We believed in the shelter of America, in the compassion of America, in the opportunity of America. We came and became Americans. We lived the words of JFK long before he uttered them - we asked not what America could do for us but what we could do for America. And we still do. We want to give and not to take," he told a room full of guests.
Mr Kenny said Irish immigrants built bridges and roads, protected the public as firefighters and police officers and cared for the sick in hospitals.
"They have entertained as poets, singers and writers. They became politicians, judges and legislators. "And as entrepreneurs they have provided hundreds of thousands of jobs for Americans including, most recently, in exciting technology companies," Mr Kenny said.
He also thanked the president for his "warm hospitality".