The Trump administration said on Friday that most foreigners seeking green cards will have to return to their home countries to apply, a remarkable change that could make it more difficult for hundreds of thousands of people to obtain permanent residency.

U.S. Citizenship and Immigration Services, the agency that oversees the legal immigration system, said it would grant green cards to people inside the country only in “extraordinary circumstances.” People applying for permanent residency, which is one step away from citizenship, will have to go through consular processing outside the country instead, according to a memo issued by the agency.

“This policy allows our immigration system to function as the law intended instead of incentivizing loopholes,” Zach Kahler, a spokesman for the agency, said in a statement. “When aliens apply from their home country, it reduces the need to find and remove those who decide to slip into the shadows and remain in the U.S. illegally after being denied residency.”

The change could upend the lives of people who entered the country lawfully through temporary visas and are seeking green cards to remain in the United States, including students, spouses of U.S. citizens and a wide range of foreign workers. The process of obtaining a green card — which gives immigrants the right to live in the country permanently and provides a path to citizenship — takes months or longer, meaning families could be separated for extended periods.

The memo was immediately met with confusion and chaos as immigration lawyers scrambled to understand which exceptions would be granted. Many also expected the policy change to be met with legal challenges.

The agency did not detail which groups would be eligible for an exception, only suggesting that refugees would not be subject. Mr. Kahler said in a statement that people who “provide an economic benefit or otherwise are in the national interest will likely be able to continue on their current path.”