A federal judge late Tuesday temporarily blocked President Trump from removing Lisa Cook from the Federal Reserve’s Board of Governors, allowing her to continue serving as she contests her recent dismissal.

Last month, Mr. Trump tried to fire Ms. Cook over allegations that she falsified documents related to her mortgages.

The decision from Judge Jia M. Cobb of the U.S. District Court for the District of Columbia dealt the Trump administration its first blow in what is likely to be a lengthy legal battle over the president’s ability to remove a Fed official “for cause,” a term generally understood to mean professional neglect or wrongdoing.

Lawyers at the Justice Department had argued in their first hearing that the president had expansive powers to determine what constitutes cause and that the court should be “highly deferential” to that interpretation. Ms. Cook, however, has neither been charged nor convicted of a crime.

The Trump administration is likely to appeal the ruling. The White House did not immediately respond to a request for comment.

The judge’s order means that Ms. Cook will be able to cast a vote when the Fed gathers for its next two-day meeting, which begins on Sept. 16. The central bank is expected to restart interest rate cuts that have been on hold since January, most likely reducing borrowing costs a quarter point.

The Fed declined to comment on the ruling. It had previously pledged to carry out any decision rendered by the court.

Mr. Trump has sought to force down borrowing costs for months, accusing Jerome H. Powell, the Fed chair, and other officials at the central bank of harming the economy by not moving quickly enough to cut rates. The Fed has kept its benchmark rate set in a range of 4.25 to 4.5 percent since January. Mr. Trump has called on the Fed to slash borrowing costs by 3 percentage points.

The president is seeking to gain a majority of support on the Fed’s board, which will give him not only greater sway over deliberations related to interest rates and the oversight of Wall Street, but also leverage over the 12 regional Fed presidents who vote on big policy decisions on a rotating basis as well as the central bank’s staff.

Ms. Cook’s lawyers said her attempted firing was politically motivated and legally dubious, citing Mr. Trump’s widening efforts to install political loyalists at the central bank.