Those unions have been a major obstacle in Mr. Trump’s effort to slash the size of the federal work force and reshape the government. With every stroke of the pen from Mr. Trump enacting new orders aimed at tightening control over the federal bureaucracy, federal worker unions have responded with lawsuits, winning at least temporary reprieves for some fired federal workers and blocking efforts to dismantle portions of the government.

Mr. Trump had framed his order stripping workers of labor protections as critical to protect national security. But the union noted that it targeted agencies across the government, some of which had no obvious national security portfolio, including the Department of Health and Human Services and the Environmental Protection Agency.

“The administration’s own issuances show that the president’s exclusions are not based on national security concerns,” the suit said, “but, instead, a policy objective of making federal employees easier to fire and political animus against federal sector unions.”