In three rulings, federal judges in New York, California and Washington State issued injunctions temporarily blocking the “public charge” rule, which would impose serious impediments to legal residency for those who use benefits such as Medicaid or those deemed likely to use them in the future.

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The rule, widely seen as an attempt to keep out immigrants who are poor or in need of help, was one of the Trump administration’s signature immigration policies - and it ran into a legal brick wall in three corners of the country on a single day.

Lawsuits filed by 21 states and the District of Columbia argued that the new regulations, which had been due to take effect on Tuesday, discriminate against low-income people from developing countries and undermine the well-being of children whose families might avoid using nutritional, health and other programs.

President Trump faced yet another legal setback in Texas, where a senior federal judge in El Paso ruled on Friday that he had acted unlawfully in announcing he would tap $3.6 billion in Pentagon money intended for military construction to build a barrier along the nation’s southwestern border.

The issues are top priorities in the administration’s efforts to curb immigration, both legal and illegal, and the rulings are likely to be swiftly appealed by the Justice Department.

“The court rulings today represent at least a temporary setback in the Trump administration’s attacks on both legal and illegal immigrants,” Steve Yale-Loehr, an immigration professor at Cornell Law School, said of the day’s decisions. “Ultimately, I predict these issues will go all the way to the Supreme Court.”

While Friday’s legal setbacks add to several recent immigration initiatives blocked by the courts, the Trump administration has nonetheless been able to roll out policies that restrict asylum, tighten requirements for skilled-work visas and slash the number of refugees the country will accept.

But the public charge regulations will not go into effect as quickly as the Trump administration desired. Two of the judges on Friday issued nationwide injunctions on enacting the policy, while the judge in California limited her ruling to the nine western states within the Ninth Circuit.

“The rule is simply a new agency policy of exclusion in search of a justification,” Judge George B. Daniels of the Federal District Court in Manhattan wrote in his ruling. “It is repugnant to the American Dream of the opportunity for prosperity and success through hard work and upward mobility.”

The regulations published by the Department of Homeland Security on Aug. 14 expand the definition of what it means to be a “public charge,” making it more difficult for immigrants to be approved for a green card if they have received benefits such as Medicaid, housing assistance or food stamps, or are deemed likely to receive them in the future.

For a nation that has long welcomed immigrants from poor countries seeking to improve their lot, the new rule could drastically change the composition of newcomers admitted to the United States. The rule would favor those who are educated and wealthy, more likely to hail from Europe than from the developing world.

The new standards would directly affect about 1.2 million applicants annually, including about 500,000 who are already in the country. But that figure does not include millions of family members and others who might also be affected. Immigration experts said the rules would disproportionately affect applicants from Africa and Latin America.

Federal immigration policy has long allowed the authorities to consider, when admitting new immigrants, the degree to which they might be a burden on the public purse. For the last 20 years, a public charge has been defined as a person “primarily dependent” on the government for subsistence, either by receiving public cash assistance or long-term institutional care.

The new regulations would lower the bar for how much assistance an immigrant might receive - or be likely to need in the future - before being deemed ineligible for legal residence.

In a statement on Friday, the White House said the court rulings prevented the government from carrying out what it said was a longstanding provision of federal law. “The rulings today prevent our nation’s immigration officers from ensuring that immigrants seeking entry to the United States will be self-sufficient,” the statement said, “and instead allow noncitizens to continue taking advantage of our generous but limited public resources reserved for vulnerable Americans.”

It said recent court rulings blocking the administration’s attempts to deport criminals, deter migrant families and tighten asylum standards, in addition to Friday’s rulings, are examples of the administration “being ordered to comply with the flawed or lawless guidance of a previous administration instead of the actual laws passed by Congress.”

The other injunctions against putting the public charge rule into effect came from Judge Phyllis J. Hamilton of the Federal District Court in Northern California and Judge Rosanna M. Peterson of the Federal District Court in the Eastern District of Washington; all of Friday’s rulings came from judges appointed by Presidents Bill Clinton and Barack Obama.

The administration had argued that the public charge rule, developed by Stephen Miller, the White House aide who is the architect of several of the government’s hard-line immigration policies, was designed to ensure that immigrants are self-sufficient and do not become a drain on the nation’s coffers.

Judge Peterson said the new regulations would undermine the interest of the states in promoting the health and well-being of their residents, as well as their financial security.

“The harms to children, including U.S. citizen children, from reduced access to medical care, food assistance, and housing support,” she wrote, are a threat to states that must reallocate resources to deal with those needs.

New York’s attorney general, Letitia James, who brought the case decided in New York, said the rule would have had a “devastating impact” on citizens and noncitizens alike.

“The history of our nation is inextricably tied to our immigrant communities, and because of today’s decision, so too will be our future,” she said in a statement. “Once again, the courts have thwarted the Trump administration’s attempts to enact rules that violate both our laws and our values.”

This month, the president also moved to deny immigrant visas to those who cannot prove that they will either have health insurance or can afford to pay for their own health care.

Mr. Trump said then that legal immigrants were three times as likely as American citizens to lack health insurance, making them a burden on hospitals and taxpayers.

The Migration Policy Institute, a nonpartisan think tank, estimated that the health insurance directive, set to take effect on Nov. 3, could exclude two-thirds of future immigrants.

“Over all, the new Trump insurance requirement could be an even stricter test for new immigrants than the public charge rule,” the think tank said in an analysis.

The public charge regulation had been roundly condemned by immigrant advocacy groups and the medical establishment, which argued that the rule would discourage immigrants from seeking government assistance when they may need help buying food or seeing a doctor.

Standards for public assistance were “never intended to exclude working-class immigrants from developing countries,” said Charles Wheeler, a director of the Catholic Legal Immigration Network, one of the plaintiffs in the case. “This ruling confirms that the American dream remains open to them.”

The policy as the administration proposed it would consider a “totality of circumstances” in assessing green card applicants based on a list of “positive” and “negative” factors. Negative factors include being unemployed, not completing high school and lacking proficiency in English. Assets, personal debts and credit score are also taken into account.

Judge Daniels was critical in his ruling of some of the weighting factors. “It is simply offensive to contend that English proficiency is a valid predictor of self-sufficiency,” he wrote.

Diminished participation in Medicaid and other programs would undermine the financial stability of immigrant families and the healthy development of their children, according to several recent studies. Nationwide, 13.5 million users of Medicaid and the Children’s Health Insurance Program, including 7.6 million children, live in a household that includes at least one noncitizen, making it possible they would decrease their use of government health benefits as a result of the rule, according to the Kaiser Family Foundation.

The complexity of the regulation and fear of being denied a green card already have sown confusion in immigrant communities. Annick Koloko, an immigration lawyer, said she had encountered immigrants who have forgone benefits in anticipation of the rule, even when they had children who were citizens and in need of help.

A client from Cameroon who has a blue-collar job pulled out of a cash assistance program that benefited her son, who is American, because she believed it would jeopardize the green-card application of her husband, who is awaiting approval in Africa.

“People are afraid,” said Ms. Koloko, who practices in New York. “The rule is extremely complex. From the moment they hear about it, they think it’s applicable to them.”

Nearly 85 percent of legal immigrants live in a family with at least one full-time worker, according to the Kaiser study, a rate higher than that of citizens. However, they are more likely than citizens to live in low-income families and work in jobs and industries that do not offer health coverage, which is why many turn to government-funded assistance such as Medicaid.

The separate court ruling on the border wall issue came from Judge David Briones of the Federal District Court in the Western District of Texas, who concluded that Mr. Trump had acted unlawfully in February by declaring a national emergency along the Mexican border.

In July, the Supreme Court allowed Mr. Trump to begin using a different appropriation, of $2.5 billion meant to combat narcotics trafficking, to build an expanded barrier along the southwestern border. The case before Judge Briones concerned $3.6 billion in separate funds that the president had hoped to tap for the wall.

Congress had allocated about $1.4 billion for the wall and specified how it could be spent, Judge Briones wrote. That “reveals Congress’s intent to limit the border barrier funding,” he wrote, a limitation Mr. Trump was not free to disregard.