Federal agencies on Monday notified legions of their employees that they can sue the government for not paying them on time during the partial shutdown of 2013.

The alerts, required under a court order, informed personnel who worked without compensation during the budget lapse that they can join a lawsuit claiming the government owes them damages for violating the Fair Labor Standards Act.

If the plaintiffs prevail, shutdowns could become far more costly for the government, putting pressure on Congress to avoid budget lapses or amend federal law so that agencies can pay their employees on time during partial closures.

The lawsuit, which appears to be the first such case brought by federal workers against their employer, seeks compensation of $7.25 for each hour worked without on-time pay between Oct. 1 and Oct. 5 of 2013, the period for which paychecks were delayed because of the 16-day budget lapse. It also asks for the full value of any overtime hours worked during that span.

The costs could total anywhere from several million dollars to more than $1 billion, depending upon how many employees join the suit and how many hours they worked.

The Justice Department declined to provide a statement Monday about the lawsuit, citing a policy of not commenting on pending litigation.

The Antideficiency Act requires the government to stop paying its employees whenever funding expires, but many personnel still have to work because their jobs are considered essential to national security. Congress has always approved back pay for those individuals after funding resumes, but the plaintiffs say they shouldn’t have to suffer through the wait.

“Many workers took months to recover financially from the impact of the government shutdown,” said Heidi Burakiewicz, an attorney with Mehri & Skalet, the Washington law firm representing the employees. “They should not be financially punished for circumstances beyond their control.”

About 1.3 million federal employees worked during the 2013 shutdown, but some are exempt from the Fair Labor Standards Act, including executives, high-level supervisors and other salaried personnel.

Five U.S. Bureau of Prisons personnel brought the original claim in October 2013, but about 5,000 federal employees have joined the action since then, Burakiewicz said.

The executive branch was dealing with circumstances beyond its control, because Congress failed to approve a funding package on time that year. The Antideficiency Act prohibits agencies from spending money during a budget lapse, even if it means forcing employees to work without pay.

But Burakiewicz suggested that lawmakers should have taken their responsibilities more seriously.

“They weren’t concerned about federal employees or violating the Fair Labor Standards Act,” she said. “The next time they think about a shutdown, all of the plaintiffs want Congress to think about the consequences.”

The government has argued that the Fair Labor Standards Act does not require payment on a particular date and that it paid the employees in full “as quickly as possible after the end of the budget impasse.”

But U.S. Court of Federal Claims Chief Judge Patricia E. Campbell-Smith ruled in August that the government violated the labor statute by failing to compensate the employees on time. She called it a “case of first impression” for the claims court.

The judge has not decided whether the workers involved in the lawsuit are entitled to damages. The plaintiffs plan to file for summary judgment by late June.

In a similar case involving California’s 1991 budget impasse, a federal appeals court ruled that the state violated the Fair Labor Standards Act but did not owe damages as long as it acted in good faith and had a reasonable belief that it was complying with the law.

The decision clarified that late payment of wages is a breach of federal law, but it left room for the government to escape paying awards to affected individuals.

Since the case is a collective-action lawsuit, employees must join the suit in order to qualify for damages. Monday’s notices are required under an order last year from Campbell-Smith.

The American Federation of Government Employees, the government’s largest union, said its legal counsel is working on an official opinion about the case.