“Let me ask those who want us to stay: How many more?” Mr. Biden said in remarks in the East Room of the White House. “How many thousands more American daughters and sons are you willing to risk? And how long would you have them stay?”

Mr. Biden said he was not declaring “mission accomplished,” but he made clear that the future of the country — including the fate of the current government and concerns about the rights of women and girls — was no longer in the hands of the American military.