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The American Library Association and a union representing more than 42,000 cultural workers nationwide have filed a lawsuit contesting the Trump administration’s deep cuts to the federal agency that supports the nation’s libraries, arguing that the cuts are already causing “irreparable harm.”

The lawsuit, filed on Tuesday by the library association and the American Federation of State, County and Municipal Employees, came days after the Institute for Museum and Library Services dismissed most of its staff of 70, fired its board and began informing state library agencies that their grants had been cut. The suit seeks a preliminary injunction reversing those actions and halting “any further steps to dissolve the agency” until the court can fully consider the issue.

The plaintiffs assert that cuts, which the suit says were ordered by the Department of Government Efficiency, threatened to disrupt the operation of libraries across the country. They argue the moves are illegal because they were undertaken without congressional approval.

“Congress is the only entity that may lawfully dismantle the agency, not the president and certainly not DOGE,” the lawsuit said.

The agency’s interim director, Keith E. Sonderling, and the White House did not immediately respond to requests for comment.

The lawsuit was filed in the U.S. District Court for the District of Columbia. Last week, the attorneys general of 21 states filed a similar lawsuit in the U.S. District Court in Rhode Island, arguing that the funding cuts violated the Constitution and federal law by usurping Congress’s power to determine how federal funds are spent.

The Institute of Museum and Library Services, created in 1996 and reauthorized in 2018 in legislation signed by Mr. Trump, has an annual budget of nearly $290 million. It provides funding to libraries, museums and archives in every state and territory.

Roughly $160 million of its funding flows directly to state library agencies, many of which rely on the money for a third to half of their budgets. In many libraries, the money supports unglamorous but crucial infrastructure like databases, circulation software and inter-library loan systems.

The institute was one of seven small federal agencies targeted by President Trump in a March 14 executive order titled “Continuing the Reduction of the Federal Bureaucracy,” which directed that the agencies be reduced to the “maximum extent consistent with applicable law.”

The moves against the library institute stirred an outcry across the library and museum worlds. In a statement on Tuesday, Cindy Hohl, the president of the American Library Association, said the cuts amounted to an attack on democracy, civic engagement and free access to information.

“These values are worth defending,” she said. “We will not allow extremists to threaten our democracy by eliminating programs at I.M.L.S. and harming the children and communities who rely on libraries and the services and opportunities they provide.”

Mr. Sonderling, the deputy secretary of labor, was named the agency’s interim director by Mr. Trump in early March, replacing Cyndee Landrum, a career library professional. Shortly after being confirmed, he visited the agency with a team that included at least one staff member of the Department of Government Efficiency, which set up offices and gained access to computer systems.

In a statement shortly after his visit, Mr. Sonderling said he would “restore focus on patriotism, ensuring we preserve our country’s core values, promote American exceptionalism and cultivate love of country in future generations.”

On March 31, the agency placed its roughly 70 employees on administrative leave, and on April 3 sent termination notices to all but a dozen. It also began sending letters to state library agencies, including those of California and Connecticut, informing them that their funding was being eliminated. On April 4, Mr. Sonderling fired all 23 members of the agency’s board, according to the lawsuit.

In recent days, the Trump administration has also moved to curb other federal cultural agencies. Last week, the National Endowment for the Humanities abruptly canceled about 1,200, or more than 85 percent, of its already-approved grants and placed more than half of its staff of about 170 on administrative leave.

Separately, Mr. Trump also issued an executive order accusing the Smithsonian Institution of falling “under the influence of a divisive, race-centered ideology” and demanding that Congress end funding for any programs there that “degrade shared American values, divide Americans by race or promote ideologies inconsistent with federal law.”

Jennifer Schuessler is a reporter for the Culture section of The Times who covers intellectual life and the world of ideas.