KABUL — Of the more than 5,700 Afghans who have applied for US visas under a program tailored for those who have supported the American war effort, 32 have been approved, the State Department says, leaving the rest in limbo as foreign forces start withdrawal.

The growing, protracted backlog threatens to undermine congressionally approved legislation, as well as the longstanding guarantee that the United States will protect Afghans whose contribution to the American mission has left them hunted and vulnerable.