A federal judge in Manhattan indicated on Monday that she was not prepared to grant President Trump exclusive first access to documents seized in F.B.I. raids on the office of his personal lawyer, and said that she was considering appointing an independent lawyer to assist in reviewing the seized materials.

Feeling her way toward a resolution of the high-stakes clash involving Mr. Trump and the federal prosecutors investigating the lawyer, Michael D. Cohen, the judge, Kimba M. Wood, did not grant Mr. Trump’s request to review the trove of materials ahead of prosecutors. But she also decided that prosecutors would not immediately have access to the materials and that Mr. Trump would ultimately receive copies of the documents that pertain to him.

The courtroom battle over what to do with the seized material came one week after federal agents, in an extraordinary move, descended on Mr. Cohen’s properties and walked away with 10 boxes of documents and as many as a dozen electronic devices, including cellphones and computer hard drives.

Lawyers for Mr. Trump and Mr. Cohen, and prosecutors with the United States attorney’s office for the Southern District of New York, had asked Judge Wood for the right to look at the documents in order to determine which among them might be protected by attorney-client privilege. That step is important because it could affect which documents prosecutors can ultimately use in the investigation.