Mr. Trump’s proclamation is a radical departure from that tradition. With the exception of children arriving without parents, officials said that all migrants who cross illegally would automatically be denied asylum. Advocates for migrants condemned the policy shift as meanspirited and unconstitutional.

“Issuing a presidential proclamation effectively denying vulnerable families protection from violence is contrary to our laws and values,” said Kevin Appleby, a senior director at the Center for Migration Studies. “In the long run, it will not deter asylum seekers who are fleeing for their lives. On this one, the emperor has no clothes.”

Across the world, nations have for years agreed to consider asylum protections for those fleeing violence and persecution, even if they cross borders illegally. Human rights advocates said on Friday that the United States should be a leader in supporting that idea.

“One thing that unites a majority of Americans is a belief in the principle of asylum,” Ali Noorani, the executive director of the National Immigration Forum, said in a statement. “Eroding that principle means eroding a defining value of our nation.”

Administration officials insisted that the new rules would remain consistent with United States obligations to the rest of the world because seeking asylum is not the only way for someone fleeing persecution to receive protection.

Officials said migrants would be allowed to seek other protections if they could prove a risk of being tortured in their home countries. However, they conceded that those claims were purposely much harder to prove and that fewer people were likely to qualify to stay in the United States than would have by receiving asylum. The only way to seek asylum will be to arrive at an official border crossing.

But officials conceded that many of the crossings from Mexico into the United States — known as ports of entry — were over capacity and already had trouble processing the number of asylum claims being made by migrants there. Under the new policy, many more are expected to arrive at the crossings.