President Biden promised to evacuate every American who wants to leave Afghanistan and said he would seek to extract Afghan allies, but he cautioned that the mission is dangerous and didn’t rule out losses, following days of chaos at Kabul’s international airport.

“I cannot promise what the final outcome will be or that it will be without risk of loss, but as commander in chief, I can assure you that I will mobilize every resource necessary,” Mr. Biden said during a speech in the East Room of the White House Friday.

The speech came at the end of Mr. Biden’s most tumultuous week as commander in chief, with the problems unlikely to go away soon. They were his first public comments in several days, and it was also the first time Mr. Biden took questions from White House reporters since the fall of Kabul, aside from a television interview this week.

Mr. Biden is facing bipartisan criticism for the chaotic U.S. exit and frenzied evacuation process, as thousands of Afghans crowd outside the perimeter of the Kabul airport. To reach the airport, Afghans and foreigners have to get past Taliban checkpoints, where Taliban fighters have been firing in the air and using violence to hold back crowds. Troops used tear gas in an effort to control the chaotic crowds Friday.