It targets tens of thousands of Central Americans who cross Mexico every month to try to enter the U.S. It also would affect asylum seekers from Africa, Asia and South America who arrive regularly at the southern border.
Legal groups argued the proposal was barred by federal law establishing how people can seek asylum.
A federal judge says the Trump administration can enforce its new restrictions on asylum for people crossing the U.S.-Mexico border while lawsuits challenging the policy play out.
U.S. District Judge Timothy Kelly in Washington has refused to grant a temporary restraining order. Another hearing on a similar suit is scheduled later Wednesday in California.