Sen. Steven Daines is announcing new legislation Monday to stop Homeland Security from offering “parole” to migrants whom the government has flagged as terrorists or who are otherwise deemed “special interest” because of their origin and travel patterns.

The bill would not only create a bar on Secretary Alejandro Mayorkas but would give states the power to go to a federal judge to force him to comply.

“Joe Biden and Senate Democrats’ refusal to secure the southern border has resulted in the loss of American lives, and as long as migrants with criminal records and potential terrorist ties are being let into the country, our national security is at risk,” said Mr. Daines, Montana Republican, who is joined by eight other GOP senators in sponsoring the bill.

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The bill comes amid growing worries over the possibility of a foreign terrorist gaining access to the U.S. through its immigration system.

FBI Director Christopher A. Wray last week raised the possibility of terrorists launching a “soft target” attack, similar to the Islamic State attack on a concert hall in Russia this spring. He also pointed to the FBI’s work in tracking down Tajik migrants who have been caught and released and only later were determined to be worrying cases.

The legislation covers “known” or “suspected” terrorists defined as those charged or identified as a terrorist by a U.S. authority, and “special interest aliens,” which it defines as those whose “travel patterns” suggest a national security risk.

Homeland Security would be prohibited from granting them parole, a special type of catch-and-release that offers tentative permission to be in the U.S. despite lacking any legal visa to do so.

The key wrinkle to the bill is that it gives state attorneys general the power to sue in federal court to stop releases that violate the law, and urges judges to speed the case.

Parole has become the Biden administration’s chief tool for catch-and-release, with Secretary Alejandro Mayorkas inventing multiple new programs that circumvent the usual immigration process to siphon people into the U.S.

Under the Obama and Trump administrations, parole averaged 5,623 people a year. Mr. Mayorkas may have paroled as many as 1.2 million in the last year alone, according to the top Republican on the Senate Judiciary Committee.

At least one of the eight Tajik men Mr. Wray referred to in his testimony is reported to have entered the U.S. under Mr. Mayorkas’ parole authority.

Mr. Daines’ bill has already drawn support from Heritage Action, the Immigration Accountability Project, the Federation for American Immigration Reform, NumbersUSA and the America First Policy Institute.

Chad Wolf, executive director of the policy institute and former acting secretary at Homeland Security, said the legislation would reverse a dangerous trend that’s emerged under President Biden.

“An unprecedented number of terrorists, special interest aliens, and cartel members have exploited the Biden Administration’s failed border strategy and been released into American communities,” he said.