Trump yesterday congratulated Varadkar on his "great victory" during a portion of the telephone conversation that the White House opened up to reporters.
The White House said later that Trump invited Varadkar to visit for St Patrick's Day next year.
Varadkar, 38, is Ireland's youngest prime minister. He's the son of an Indian immigrant and the first openly gay politician in the post.
Varadkar is also a doctor who has held three previous Cabinet posts. He defeated a rival in a contest to replace Enda Kenny, who resigned.
Victory in an electoral college system is something Trump understands. That's how he was elected president last November.
"I just want to congratulate you. That was a great victory that you had," Trump said.