WASHINGTON — The Trump administration is close to recommending that all Americans wear cloth masks if they go out in public, a change in position that reflects new concerns that the coronavirus is being spread by infected people who have no symptoms and new data suggesting the United States is not yet slowing the rate of infections.

At a White House briefing Thursday evening, both President Trump and Vice President Pence said that new guidance on masks would be issued by the Centers for Disease Control and Prevention in the coming days. But the comments of both Mr. Trump and a top official on the administration’s coronavirus response task force during the session suggested that the issue hasn’t been entirely resolved within the administration.

“If people want to wear them, they can,” President Trump said, declaring that while the administration was “coming out with regulations” on mask wearing soon, whether to follow them was a personal choice.

Dr. Deborah Birx, the White House’s coronavirus response coordinator, sounded a sharper note of caution, saying that she did not want Americans to get a false sense of security from wearing masks. Washing hands and keeping six feet away from other people were more protective steps, she said, and suggested that the still-unannounced new guidance remained under debate.