Migrants who passed through another country first would be ineligible for asylum at the U.S. border, with some exceptions.

The Trump administration moved to dramatically limit Central American migrants’ ability to seek asylum at the U.S. border with Mexico, an escalation of the president’s push to stem the flood of border crossers that is severely straining the U.S. immigration system. Under the rule published online on Monday, with limited exceptions, migrants who pass through another country first must seek asylum there rather than at the U.S. border, where they will be ineligible to do so. The vast majority of asylum seekers at the U.S.-Mexico border come from Central America, passing through Mexico, and in some cases Guatemala, first. The rule, issued by the Department of Justice and the Department of Homeland Security, takes effect Tuesday. Trump officials said the Immigration and Nationality Act gives the attorney general the authority to set new limitations on who can seek asylum.

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