The speaker’s office confirmed that Ms. Pelosi, who is vaccinated and boosted, had received a negative P.C.R. test result on Thursday morning, and would continue to test regularly and follow C.D.C. guidelines, though it was not clear which ones. It was also unclear whether the Office of the Attending Physician considered Ms. Pelosi, 81, to be a close contact of Mr. Martin.

Ms. Pelosi appeared at her weekly news conference on Thursday, saying that she was tested nearly every day. Mr. Martin remained masked until food was served, she said, and was pulled aside during the appetizer course about his positive test.

“We’re very, very sad that on St. Patrick’s Day, the taoiseach has this diagnosis,” she said at her indoor news conference, where she removed her mask to speak and take questions.

The scheduled lunch — the Friends of Ireland Luncheon on Capitol Hill — proceeded on Thursday without Mr. Martin. Ms. Pelosi addressed the room, where lawmakers sat at round tables, while introducing Mr. Biden, who sat on a stool a few feet away. Neither wore a mask, and there were few face coverings in the room.

“America has been blessed by Irish children, and one of those Irish children is now the president of the United States,” Ms. Pelosi said, just before they shook hands and Mr. Biden took the lectern. He did not stay for lunch.

In a tradition going back to 1952, Irish ambassadors or political leaders present the American president with a bowl of shamrocks on or around St. Patrick’s Day, usually in the White House. The tradition is valued in Ireland, and by many Irish Americans, as a sign of the close ties between the two countries.

Mr. Martin may now never visit the Oval Office in his official capacity: His first scheduled visit last year was canceled because of the pandemic and, as part of a coalition deal with two other Irish political parties, he is expected to hand over the prime ministership before next March.

On Wednesday, Claire Cronin, the U.S. ambassador to Ireland, said on Twitter that she canceled her plans to join Mr. Martin on his trip to Washington because she had tested positive for the coronavirus.

Emily Cochrane contributed reporting from Washington, and Adeel Hassan and Alyssa Lukpat from New York.