WASHINGTON—A divided Supreme Court allowed the Trump administration to begin implementing rules that make it easier for the government to deny limited-income immigrants residency or admission to the U.S. because they use public-assistance programs or might use them in the future.

The court, in a written order Monday, granted the administration’s emergency request to start enforcing the rules for now, a move that nullifies an order by a federal appeals court that blocked the immigration restrictions while litigation was ongoing.

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