An applicant who speaks English, shows formal letters of support and has private health insurance would be more likely to be approved than someone whose financial situation suggests they would probably need housing vouchers or enroll in Medicaid in the future if they were given a green card.

Immigrants who have incomes equal to or greater than 250 percent of the official poverty line — about $64,000 for a family of four — are not likely to be declared public charges, according to the new regulation. Immigrants with incomes far less than that who are seeking green cards will have to prove that they will not require public benefits in the future.

Over time, administration officials hope that the tough policy will shift the composition of the American immigration system by favoring wealthier immigrants.

Asked about the 1903 plaque on the Statue of Liberty that invites “your tired, your poor, your huddled masses,” Mr. Cuccinelli said: “I’m certainly not prepared to take anything down off the Statue of Liberty. We have a long history of being one of the most welcoming nations in the world.”

But immigration advocates reacted with anger at the announcement, describing it as a cruel policy that they said was already causing immigrants around the country to abandon housing and medical benefits because they were concerned about the impact that using them might have on their immigration status or the status of someone in their family.

“Shame on the Trump administration for expanding a rule with racist roots in a shameful ploy to rig the immigration system for the wealthy,” said Cynthia Buiza, the executive director of the California Immigrant Policy Center. “We thank all who stood up against the administration’s hate-filled agenda, and we will continue to fight for our values of community, compassion and common humanity.”

The fear touched off by the new rule is illustrated by Maria, a 28-year-old woman from Colombia who is five months pregnant and asked that her last name not be used because she feared reprisals by American immigration officials. A couple of weeks ago she reached out to her lawyer for advice after she started seeing coverage of the draft version of the public charge rule. Her husband, a childhood friend from Colombia, is an American citizen, and she is in the United States on a tourist visa while she applies for a green card with him as a sponsor.