"Congratulations on your great victory," Trump told Varadkar, as the US leader sat at the Resolute Desk in the Oval Office for the telephone talks.
"We have so many people from Ireland in this country -- I know so many of them, I feel like I know all of them."
A small group of journalists was allowed to witness the start of the talks -- an unusual allowance by the White House.
The 38-year-old Varadkar, who was born in Dublin to an Indian immigrant father and an Irish mother, is seen as progressive on social issues such as gender equality and abortion rights.
Varadkar took office as prime minister, or taoiseach, earlier this month after winning the leadership of Ireland's ruling centre-right Fine Gael party.