The Justice Department has indicated that it will not force a New York Times reporter to divulge his confidential source, potentially eliminating a significant element of a lengthy battle over press freedoms. But important questions remained as the deadline of a Tuesday court hearing approached.

A Justice Department official, speaking anonymously, told news organizations on Friday that prosecutors may give up trying to compel the reporter, James Risen, to name his source. The official also was quoted as saying that the Justice Department still might subpoena Mr. Risen to testify at the trial of Jeffrey A. Sterling, a former C.I.A. officer accused of disclosing classified information that appeared in a 2006 book by Mr. Risen, “State of War.”

“This issue is hardly resolved,” said Dean Baquet, the executive editor of The New York Times. “One of the country’s best investigative reporters could still be put in the position of having to testify about a source.”

Unless there is agreement about what questions Mr. Risen would be asked, it is not clear that the offer from the Justice Department would resolve what has been widely viewed as an important fight over government secrets and press freedom. The Justice Department must say in court on Tuesday what it plans to do about the subpoena.