They said the children of immigrants who are in the United States legally could be the most vulnerable. Indeed, immigrant parents who work low-wage jobs and rely on assistance may need to remove their children from the programs to keep their families together in the United States. Unauthorized immigrants are ineligible for nearly all public benefits.

Trump administration officials say the rule is intended to promote fiscal responsibility.

“Self-sufficiency has been a basic principle of United States immigration law since this country’s earliest immigration statutes,” the proposal says. It remains United States policy that “the availability of public benefits not constitute an incentive for immigration to the United States.”

The government has traditionally considered someone who relies on government cash assistance for more than half of his or her income a public charge. Now, however, officials will take into account whether an individual or a family has received any of an assortment of noncash public benefits, such as aid from the Supplemental Nutrition Assistance Program, formerly known as food stamps; the Section 8 program, which provides housing assistance; or the Medicare prescription drug program for older adults.

“This is long overdue,” said Mark Krikorian, the executive director of the Center for Immigration Studies, whose research supports decreased immigration. “This country has defined public charge in a fictional way in order to facilitate high levels of low-skilled immigration. But this is simply a 21st-century definition of what public charge is.”

Officials said that the new rule did not apply to refugees or asylum seekers who enter the country, or to legal immigrants who serve in the military. Cash or other assistance given to the immigrant victims of natural disasters would not be counted against them.

Critics of the new rule argue that it deviates from longstanding precedent and from Congress’s original intent for the public-charge statute. They also say it violates states’ rights to provide benefits to children and immigrants experiencing short-term crises.

Nearly 20 million children in immigrant families could be affected by the policy changes, according to a report by the Kaiser Family Foundation that examined a draft of the new rule that was even broader than the one announced on Saturday. Almost nine in 10 of those children are United States citizens.