The Trump administration has begun enforcing radical new restrictions on who qualifies for asylum as tens of thousands of migrants wait on the Mexican border, seeking refuge.

The new U.S. policy would effectively deny asylum to nearly all migrants arriving at the southern border who aren't from Mexico. It would disallow anyone who passes through another country without first seeking and failing to obtain asylum there.

RELATED: VERIFY: No, asylum seekers don't get more money than Social Security recipients

RELATED: Supreme Court allows broad enforcement of asylum limits

The rule will fall most heavily on Central Americans, mainly Hondurans and Guatemalans, because they account for most people arrested or stopped at the border.

But it also represents an enormous setback for other asylum seekers, including large numbers of Africans, Haitians and Cubans who try to enter the United States by way of the Mexican border.

Advocates had sued and the policy was on hold, but the Supreme Court ruled Wednesday it could be implemented while the challenge is heard.

Most asylum seekers pass an initial screening called a "credible fear" interview. Under the new policy, they would fail the test unless they sought asylum in at least one country they traveled through and were denied.

A spokeswoman for the Homeland Security agency that conducts asylum interviews says the policy will be retroactive to July 16, when the initial rule was announced.