The city of San Francisco and nearby Santa Clara County sued President Donald Trump's administration Tuesday, seeking to block a new rule that would drastically reduce legal immigration by denying visas to poor migrants.

Also, California Attorney General Xavier Becerra confirmed Tuesday night the state also plans to file its own lawsuit against the green card rule.

"We think it's un-American and unlawful, and we believe it would destroy good portions of our economy if we allowed a rule like this to take effect," Becerra told CNN's Anderson Cooper. "We rely on the hard work of people who understand what it means to toil and to somehow overcome to be able to have a state like California that's become the number one state economically for this country, and the fourth- or fifth-largest economy in the world.

"We need people that want to show they earned a place in America."

Becerra added he does not expect the new policy to stand, not only as an attorney general but as an American and as a son of immigrants.

"The process by which it's being implemented is we believe illegal," he said. "The terms it would impose on people we believe are illegal, and we also believe that it violates the Constitution's equal protection, so under the laws of this country, we don't believe that rule will stand."

Some experts say the new rule could cut legal immigration in half by denying visas and permanent residency to hundreds of thousands of people if they fail to meet high enough income standards or if they receive public assistance such as welfare, food stamps, public housing, or Medicaid.

"This illegal rule is just another attempt to vilify immigrants," San Francisco City Attorney Dennis Herrera said in a statement. Trump has made efforts to curb both legal and illegal immigration, an issue he has made a cornerstone of his presidency and one that he has stressed again as the campaign for the 2020 presidential election heats up.

The rule, unveiled Monday and to take effect Oct. 15, expands the definition of a public charge, allowing denials to visa applicants who fail to meet income requirements or who receive public assistance.

"The final rule rejects the longstanding, existing definition of public charge, and attempts to redefine it to include even minimal use of a much wider range of non-cash benefits," said the lawsuit, filed in U.S. District Court in San Francisco.

"The final rule will worsen the health and well-being of the counties' residents, increase risks to the public health, undermine the counties' health and safety-net systems, and inflict significant financial harm," the suit said.

San Francisco is both a city and a county. Santa Clara County includes the city of San Jose and various other parts of Silicon Valley.

The suit names U.S. Citizenship and Immigration Services, the Department of Homeland Security and their directors as defendants. The former agency declined to comment and the latter did not immediately respond to a request for comment.

The suit claims the new rule violates the Immigration and Nationality Act of 1965 by contradicting the longstanding definition of public charge as a person "primarily" dependent on public assistance for survival.

The suit also claims the new rule would split families, undermining immigration laws to prioritize family unification; misapplies the intent of Congress on the description of self-sufficiency of immigrants; and runs contrary to the statutes governing SNAP, also known as food stamps.

The National Immigration Law Center said it also will file a lawsuit to stop the rule from taking effect. The attorneys general of California and New York have also threatened to sue.

Newsmax writer Sandy Fitzgerald contributed to this report.