The Justice Department said on Monday that it was open to accepting one of former President Donald J. Trump’s proposed candidates for the job of an independent arbiter to review thousands of documents seized last month by the F.B.I. from Mr. Trump’s residence in Florida.

In a brief court filing, prosecutors said they would not object if the judge presiding over the case appointed Judge Raymond J. Dearie of the Federal District Court in Brooklyn as special master to oversee an evaluation of the trove of sensitive materials seized from Mr. Trump’s estate, Mar-a-Lago.

Mr. Trump’s lawyers and lawyers for the Justice Department are also engaged in a separate court fight over how a potential special master should review the seized documents. Mr. Trump wants an expansive review that would scrutinize all of the materials for items protected by attorney-client or executive privilege; the Justice Department wants a narrower review excluding about 100 documents bearing labels marking them as classified.

The decision by the Justice Department to formally accede to one of Mr. Trump’s choices for the special master job was a pullback from the position it set forth on Friday when prosecutors and Mr. Trump’s lawyers filed competing candidates for the position.

Initially, the Justice Department suggested two retired federal judges for the post: Barbara S. Jones, who formerly sat on the Federal District Court for the Southern District of New York, and Thomas B. Griffith, who formerly sat on the Court of Appeals for the District of Columbia Circuit.

The Trump legal team countered with the semiretired Judge Dearie, who sits as a part-time senior judge on the Federal District Court for the Eastern District of New York, and Paul Huck Jr., a former deputy attorney general in Florida. Judge Dearie, who was appointed by President Ronald Reagan, has also served on the Foreign Intelligence Surveillance Court overseeing highly classified matters.

In their filing on Monday, lawyers for the Justice Department said that Ms. Jones, Mr. Griffith and Judge Dearie all had “substantial judicial experience” and were qualified for the special master job. The Justice Department said that Mr. Huck, a former deputy attorney general in Florida, “does not appear to have similar experience.”

Ultimately, the judge overseeing the case, Aileen M. Cannon of the Federal District Court in the Southern District of Florida, will choose the special master.