Israeli authorities are investigating a civilian who has been working over the past year in the office of Prime Minister Benjamin Netanyahu and is suspected of illegally obtaining and leaking classified documents to the news media.

The documents helped support Mr. Netanyahu’s reasoning for adding tough new conditions for a cease-fire deal with Hamas over the summer, amid intense public pressure for a deal to release Israeli hostages and end the fighting in Gaza.

The case has roiled Israel, where critics have accused Mr. Netanyahu of torpedoing a deal to return hostages and of prolonging the war in Gaza for political reasons. Key members of his governing coalition had threatened to quit if he made concessions to Hamas.

On Sunday, an Israeli court partially lifted a gag order to identify Eliezer Feldstein, who was hired last year to work as a spokesman in Mr. Netanyahu’s office, as a suspect in the case. Three other suspects in the case are members of the military and security establishment, according to the court, and have not been publicly named.

The investigation has revolved around the publication and manipulation of real and purported intelligence information in media outlets abroad, according to Israeli news reports and to an Israeli official who was not authorized to discuss sensitive information, including the case. The London-based Jewish Chronicle published — and then retracted — a report claiming Hamas was planning to smuggle Israeli hostages from Gaza to Egypt. A classified document that was leaked to the German newspaper Bild claimed that Hamas was trying to manipulate the Israeli public and wanted to draw out the negotiations.

How did this all get started?

On Sept. 1, the Israeli military announced that six Israeli hostages had been found dead in a tunnel in Gaza after being fatally shot by their captors, prompting a surge of mass protests and a wave of national anger and grief.