NORFOLK, Va. — Virginia Attorney General Mark Herring joined a lawsuit challenging a Trump administration rule that'll allow immigration officials to deny green cards to migrants who use public assistance, including food stamps or housing vouchers.

Thirteen states total filed the federal lawsuit Wednesday in Richland, Washington. It follows a similar lawsuit Tuesday by two California counties.

"We have brought this suit because Ken Cuccinelli and Donald Trump are trying to unilaterally keep out immigrants who they deem unworthy," said Herring.

Under new rules unveiled this week, Citizenship and Immigration Services will consider whether applicants have received public assistance among other factors such as education to determine whether to grant legal status.

Herring and the other attorneys general argue the expansion will cause "irreparable harm" and deter noncitizens from seeking "essential" public assistance.

The lawsuit alleges the new rule jeopardizes the effectiveness and the cost of health care programs like Medicaid. It points out that eligible people, including citizens, will disenroll or not enroll at all because they fear their family may be in jeopardy.

"When individuals and families don’t have access to healthcare, then they get sicker and eventually they’ll present themselves at the emergency room and get care at a much more expensive level and that will cost all of us," said Herring.

But the Trump Administration says immigrants must be financially self-sufficient.

"I don't think it's fair to have the American taxpayers paying for people to come into the United States," said President Trump.

The lawsuit names the US Department of Homeland Security and its acting secretary, Kevin McAleenan, as well as U.S. Citizenship and Immigration Services and its acting director, Ken Cuccinelli. 

Cuccinelli was Virginia's attorney general prior to Herring.

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In addition to Virginia, the other states involved in the lawsuit are Colorado, Delaware, Illinois, Maryland, Massachusetts, Michigan, Minnesota, Nevada, New Jersey, New Mexico, Rhode Island, and Washington.

The Associated Press contributed to this report.