Two Democratic former members of the Federal Trade Commission sued President Trump on Thursday over his decision to fire them from the agency, accusing him of an illegal overreach of executive power.

Mr. Trump fired the Democratic commissioners, Rebecca Kelly Slaughter and Alvaro Bedoya, on March 18, upending the consumer protection agency, which is typically run by three members from the president’s party and two from the opposing party.

In a lawsuit filed in the United States District Court for the District of Columbia, lawyers for Ms. Slaughter and Mr. Bedoya argued that Mr. Trump’s dismissals of them were without cause and violated federal law. They cited a 1935 Supreme Court precedent that said the president may not fire independent regulatory boards members solely over policy disagreements.

“In short, it is bedrock, binding precedent that a president cannot remove an F.T.C. commissioner without cause,” the lawsuit said. “The president’s action is indefensible under governing law.”

The White House, which did not immediately respond to a request for comment, previously said that “President Trump has the lawful authority to manage personnel within the executive branch.”

The lawsuit was the latest legal battle to erupt over Mr. Trump’s attempts to expand the power of the presidency. In recent months, more than 50 court rulings have in many cases temporarily halted actions taken by the administration, ranging from its aggressive stance on deportations to its firing of civil servants.

The legal battles have also affected regulators that Congress set up to be independent from direct White House control. While regulators are appointed by the president, many have traditionally had wide latitude to determine the direction of their agencies.

But Mr. Trump earlier fired Gwynne Wilcox, a Democrat on the National Labor Relations Board, who was reinstated by a federal court this month. The administration has appealed that ruling.

Mr. Trump also signed an executive order last month that affected the F.T.C., the Securities and Exchange Commission, the Federal Communications Commission and the National Labor Relations Board. The executive order instructed those agencies to submit proposed regulations to the White House for review, as well as declaring that they must accept as binding the interpretations of the law made by the president and the Justice Department, among other measures.

Ms. Slaughter and Mr. Bedoya’s lawsuit also named the two Republican F.T.C. commissioners — the agency’s chairman, Andrew Ferguson, and Melissa Holyoak — as defendants. They also named the agency’s executive director, David B. Robbins.

The 1914 law that established the F.T.C. says commissioners can be removed from the five-member board for “inefficiency, neglect of duty or malfeasance in office.” The Supreme Court reinforced those protections in the 1930s when President Franklin D. Roosevelt tried to fire a member of the F.T.C.

In a letter sent on behalf of Mr. Trump last week informing one of the commissioners of the termination, the White House said the protections established by the Supreme Court’s ruling didn’t apply to those who led the F.T.C. today.

Mr. Ferguson said in a statement last week that he had “no doubts” about the president’s constitutional authority to remove his colleagues. The F.T.C. did not immediately respond to a request for comment on the lawsuit.

In the lawsuit, lawyers for Ms. Slaughter and Mr. Bedoya said the two have been “denied access to their offices” and were now listed as former members of the commission on the F.T.C.’s website. Their staff have also been put on administration leave, according to the lawsuit.

The F.T.C. has been responsible for some of the biggest showdowns between corporate America and the federal government. In April, the agency is scheduled to face off against Meta, the owner of Facebook, Instagram and other apps, at an antitrust trial over whether the tech giant illegally stifled nascent competitors when it bought Instagram and WhatsApp.

The F.T.C. has also filed lawsuits against Amazon, arguing it made it hard for consumers to cancel its Prime subscription service and squeezed small merchants that use its site.

Under Mr. Ferguson, the agency has increasingly turned its focus to the big online platforms’ power over speech and discourse. Last month, the agency began soliciting comments from people and business who said their posts had been improperly removed by social media sites.