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.

The court’s action came on a 5-to-4 vote, splitting the justices along ideological lines, with conservatives in the majority. As is its custom when it issues emergency orders, the court didn’t explain its reasoning.

Announced last August by the Department of Homeland Security, the rules effectively expand the pool of people considered likely to become a “public charge” under U.S. immigration law. If an immigrant makes use of a public assistance program, such as housing assistance, food stamps or Medicaid—or an immigration officer estimates he or she might in the future—the person could be denied a green card or barred from the U.S. altogether.

The rules have the potential to reshape the type of immigrants who are allowed into the U.S. and significantly curb the number of people granted permanent residence each year.

The White House called the court’s order a “massive win for American taxpayers, American workers and the American Constitution. This decision allows the government to implement regulations effectuating longstanding federal law that newcomers to this country must be financially self-sufficient.”

Foreigners seeking immigration status in the U.S. generally have to show they have enough financial resources to keep them from relying on government programs that assist poor Americans. The denial of immigration visas on “public charge” grounds has increased during the Trump administration, even before the new rules.

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Immigrants aren’t eligible for the vast majority of public assistance programs in the U.S., and most would feel the rule’s impact through a test immigration officers must follow to determine whether they might in the future become dependent on a public benefit.

The test will vet applicants on a series of factors, such as their English-speaking ability, their educational attainment, their health, and whether their income is less than 125% of the federal poverty level. Scoring poorly on any of these factors could make it less likely for an immigrant, applying from within the U.S. or abroad, to qualify for permanent residency.

The Migration Policy Institute, a nonpartisan Washington think tank, estimates that a majority of future applicants from Latin America and Africa could be denied under the new test.

“Never before have we said, you have to be comfortably middle class before you come to America,” said Doug Rand, co-founder of Boundless Immigration who advised on immigration policy during the Obama administration. “That’s what we’re saying now.”

Most public assistance programs in the U.S., such as Medicaid, aren’t available to immigrants until they have held permanent residence status for at least five years.

Still, immigrant advocates fear that the new policy could drive many more immigrants, especially unauthorized immigrants with U.S. citizen children, to forgo public benefits altogether.

“The administration is counting on fear to amplify the damage,” said Olivia Golden, executive director of CLASP, an anti-poverty advocacy organization.

Several judges issued preliminary rulings last October that blocked the Trump administration policy. Some, but not all, of those rulings had been put on hold by higher courts.

In the case that prompted the Trump administration’s emergency appeal, a federal judge in New York found the rule departed from longstanding policy without legal justification and “is repugnant to the American dream.”

U.S. Solicitor General Noel Francisco argued in Supreme Court papers that the regulation was a lawful and reasonable exercise of executive authority. Blocking the rules, even during litigation, harmed the government by forcing it to grant immigration status to people who shouldn’t have it, Mr. Francisco said.

Mr. Francisco also said a court in one district shouldn’t be able to block a regulation across the U.S.

The Supreme Court’s action isn’t a final ruling on the merits of the case, but it does suggest the Trump administration faces at least decent legal prospects of winning.

The court issued the order Monday afternoon while Chief Justice John Roberts was presiding over President Trump’s impeachment trial in the Senate. The order was unsigned, but the court’s four liberal justices—Ruth Bader Ginsburg, Stephen Breyer, Sonia Sotomayor and Elena Kagan—dissented, saying in one sentence that they would have ruled against the Trump administration’s request.

That means Chief Justice Roberts was in the majority with his four conservative colleagues: Justices Clarence Thomas, Samuel Alito, Neil Gorsuch and Brett Kavanaugh.

Justice Gorsuch wrote a separate concurrence, joined by Justice Thomas, to register his objections to the increasing practice of lower courts of limited geographic scope issuing injunctions that block a government policy nationwide.

The case before the high court stemmed from lawsuits brought by the states of New York, Connecticut and Vermont, as well as New York City and organizations that assist immigrants.

New York Solicitor General Barbara Underwood argued the administration’s definition of who is a public charge “is a stark departure from a more-than-century-long consensus that has limited the term to individuals who are primarily dependent on the government for long-term subsistence.”

Monday’s high court action means the Trump administration can move forward with the public-charge rules everywhere but Illinois, where a different legal ruling remains in place for now.

The case marks the latest of nearly two dozen instances in which the administration has sought emergency intervention from the Supreme Court after lower courts stymied its policies and enforcement plans. The high court has granted the administration room to implement several high-profile initiates, including tighter immigration policies, but not others, including when it declined to block a trial on the administration’s now-abandoned plans to ask about citizenship on the 2020 census.

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Write to Brent Kendall at brent.kendall@wsj.com and Michelle Hackman at Michelle.Hackman@wsj.com