A flurry of high-profile coronavirus cases in the nation’s capital — including in people who have been around President Biden — has raised new questions about the trajectory of the two-year-old pandemic, even as the White House has signaled confidence in the country’s ability to resume normal activities.

On Thursday, Mr. Biden canceled face-to-face meetings with Prime Minister Micheal Martin of Ireland after the prime minister received a positive result from a coronavirus test during a gala event on Wednesday night that both men attended.

In the past week, Doug Emhoff, the husband of Vice President Kamala Harris, tested positive for the virus, as did former President Barack Obama. At least nine House Democrats received positive tests this week after a party retreat in Philadelphia and late-night voting at the Capitol.

White House officials said Mr. Biden, 79, had not been in close contact with anyone who tested positive and did not appear worried about his safety. They said that the administration was monitoring a highly transmissible subvariant known as BA.2, which is spreading rapidly in parts of China and Europe, but that there appeared to be little reason to think there would be a U-turn back to social distancing and universal mask wearing in the United States.