Donald Trump plan to make Republic of Ireland America's EU base
The Donald Trump administration plans to use the Republic of Ireland as an increasingly important ally in Europe as the UK prepares to depart the European Union.
And the White House is also intending to reach out to Mr Kenny's successor as Taoiseach.
A senior White House official indicated the warm reception afforded Mr Kenny is a clear sign the Trump administration wants to work more closely with Ireland. "With Brexit, Ireland comes more into play for us in Europe," the source told the Irish Independent.
"There have been 12 state visits since the President took over, and some have been 45 minutes. But he has attended three separate events with Kenny - it's unprecedented that he'd give over a full day like that."
On Friday, Mr Trump held a far more frosty meeting at the White House with German Chancellor Angela Merkel.
Separately, White House Press Secretary Sean Spicer reiterated the administration's intention to strengthen its ties with Ireland.
Mr Spicer also stressed how the White House "looks forward to meeting with whoever the Irish people choose as his [Mr Kenny's] successor".
But Mr Kenny is now suggesting he will not be dealing with the leadership issue when he returns from the US and plans to cling to power for longer.
Meanwhile, Mr Kenny suggested he would refuse to sign off on any Brexit deal that involved a return to a hard border with Northern Ireland.