Israel’s government late Tuesday signed off on an American-brokered deal with the Hamas terrorists holding some 240 hostages at Gaza that could see the release of scores of women and children being held in exchange for a brief pause in the conflict now raging in Israel.

The deal calls for a four-day cease-fire, during which Israel will halt its military offensive in Gaza while Hamas frees “at least” 50 of the roughly 240 hostages it and other militants are holding, Prime Minister Netanyahu’s office says. The first hostages to be released are women and children.

“The government of Israel is committed to bringing all of the hostages home. Tonight, the government approved the outline for the first stage of achieving this goal,” the office said in a statement.

Mr. Netanyahu, however, said the war itself will not stop before all the hostages are released. “We are at war, and we will continue the war,” he told reporters ahead of a late-night cabinet meeting. “We will continue until we achieve all our goals.”

According to reports in the Israeli press, the agreement includes a five-day halt in Israel’s offensive in Gaza and the release of as many as 50 hostages held by Hamas in exchange for some 150 Palestinian prisoners held by Israel.

The Israeli government statement said the truce would be extended an extra day for every additional 10 hostages released by Hamas.

Israel’s Channel 12 TV said the first releases would take place Thursday or Friday and continue for several days. Among those slated to be released are 30 children, eight mothers, and 12 other women.

Channel 12 reports that Hamas claims to have 210 of the roughly 240 hostages taken on October 7, including about 40 children. The group says, however, that it cannot immediately locate the additional 10 children, who may be held by another terrorist group in the region, Islamic Jihad.

Mr. Netanyahu said the deal also includes guarantees that representatives of the Red Cross would be allowed to visit the Israeli hostages still remaining in Gaza and provide medicine if needed.

Citing anonymous Israeli officials, the network said the truce could be extended and additional Palestinian prisoners released if there were additional hostages freed. Israel, the United States and Qatar, which supports Hamas, negotiated for weeks over the deal.

Inside Gaza, the front line of the war shifted Tuesday to the Jabaliya neighborhood, a densely built district of concrete buildings near Gaza City. Israel has bombarded the area for weeks, and the military said Hamas fighters have regrouped there and in other eastern districts after being pushed out of much of Gaza City.

Residents of Jabaliya said there was heavy fighting as Israeli forces tried to advance under the cover of airstrikes. The Israeli military said strikes hit three tunnel shafts where fighters were hiding and destroyed rocket launchers. Footage released by the military showed Israeli soldiers patrolling on foot as gunfire echoed around them.

Most of Gaza’s population of 2.3 million have crowded into the southern section of the Gaza Strip, where Israeli strikes have continued and where the military says it intends to extend its ground invasion.

Before the hostage deal was announced, a spokesman for the Israel Defense Forces, Rear Admiral Daniel Hagari, said it would not impact the military’s ultimate goal of eliminating Hamas.

“The goal of returning the hostages is significant,” Mr. Hagari told reporters in Tel Aviv Tuesday. “Even if it results in the reduction of some of the other things, we will know how to restore our operational achievements.”

The Associated Press contributed to this report.