Mr Kenny also described Ireland as a "microcosm" of Europe that had made really difficult decisions in recent years, and Mr Trump was "very complementary of the people of Ireland" for their role in the economic recovery.
A large part of the talks were taken up by immigration issues with Mr Trump expressing surprise that there are only 50,000 undocumented Irish in the US.
Taoiseach Enda Kenny has rebuffed Nigel Farage's call for him to apologise to President Donald Trump for accusing him of using racist language.
However, the issue of taxation was not discussed despite the proposed lowering of corporate tax in the US causing serious concern in Ireland during Trump's campaign and early days in office.
At the end of meeting both politicians agreed to continue "friendly, constructive engagement".
Mr Kenny said he told the President that in Ireland "invitations are always returned"
Mr Trump indicated he will come to Ireland during his presidency.