In the months since President Biden imposed sweeping restrictions on asylum at the U.S.-Mexico border, the policy appears to be working exactly as he hoped and his critics feared.

The number of people asking for haven in the United States has dropped by 50 percent since June, according to new figures from the Department of Homeland Security. Border agents are operating more efficiently, administration officials say, and many of the hot spots along the border, like Eagle Pass, Texas, have calmed.

The numbers could provide a powerful counternarrative to what has been one of the Biden administration’s biggest political vulnerabilities, particularly as Vice President Kamala Harris, the Democratic presidential nominee, tries to fend off Republican attacks.

But migrant activists say Mr. Biden’s executive order is weeding out far too many people, including those who should be allowed to have their cases heard, even under the new rules. They say the figures are so low in part because of a little-noticed clause in the new policy, which changed how migrants are treated when they first arrive at the border.

Under the new rules, border agents are no longer required to ask migrants whether they fear for their lives if they are returned home. Unless the migrants raise such a fear on their own, they are quickly processed for deportation to their home countries.