The "Late Night" also made a wild prediction about how Trump's presidency may end.
The president refused to visit the capital, Dublin, and instead insisted that the prime minister meet him at or near his Doonbeg golf course on the Atlantic Coast.
Trump tried to hold the meeting at one of his golf resorts, but Irish officials balked at promoting one of his properties.
A meeting in a Trump hotel is "unseemly" and the choice of venue should be up to Irish leader Leo Varadkar, an Irish government source tells CNN.
The vice president of the United States invited Irish Taoiseach Leo Varadkar to bring his partner, Dr. Matt Barrett.
It was a powerful gesture, as LGBTQ groups had been banned from the parade until 2015.
Leo Varadkar's first official Northern Ireland visit included a "Pride Breakfast."
Ireland's prime minister Leo Varadkar upstaged his Canadian counterpart in the sock stakes during their first official meeting.
Trump was put on hold for at least 90 seconds, then he pulled a reporter into the chat.
The 38-year-old son of an Indian immigrant will be the youngest person to hold office.
Leo Varadkar's victory would show another face of the Catholic country.