TEL AVIV, Israel — Israel and Hamas agreed to extend their cease-fire for two more days past Monday, the Qatari government said, raising the prospect of a longer halt to their deadliest and most destructive war and further exchanges of militant-held hostages for Palestinians imprisoned by Israel.

The announcement, made by Qatari Foreign Ministry spokesman Majid Al Ansary in a post on X, came on the final day of the original four-day truce between the warring sides. A fourth swap of hostages for prisoners under that deal was expected later Monday.

Israel has said it would extend the cease-fire by one day for every 10 additional hostages released. After the announcement by Qatar — a key mediator in the conflict, along with the United States and Egypt — Hamas confirmed it had agreed to a two-day extension “under the same terms.”

But Israel says it remains committed to crushing Hamas’ military capabilities and ending its 16-year rule over Gaza after its Oct. 7 attack into southern Israel. That would likely mean expanding a ground offensive from devastated northern Gaza to the south, where hundreds of thousands of Palestinians have crammed into United Nations shelters, and where dire conditions persist despite the increased delivery of aid under the truce.

Israel will resume its operations with “full force” as soon as the current deal expires if Hamas does not agree to further hostage releases, government spokesperson Eylon Levy told reporters on Monday. Israel has said that, in addition to dismantling Hamas. freeing the rest of the captives is a top priority.

So far, 58 hostages have been released during the current truce, including 39 Israelis. Before the truce, four hostages were freed, another was rescued and two were found dead inside Gaza. Israel has released 117 Palestinians from prison since the truce began.

After weeks of national trauma over the roughly 240 people abducted by Hamas and other militants, scenes of the women and children reuniting with families have rallied Israelis behind calls to return those who remain in captivity.

“We can get all hostages back home. We have to keep pushing,” two relatives of Abigail Edan, a 4-year-old girl and dual Israeli-American citizen who was released Sunday, said in a statement.

Hamas and other militants could still be holding up to 175 hostages, enough to potentially extend the cease-fire for two and a half weeks. But those include a number of soldiers, and Hamas is likely to make much greater demands for their release.

On Sunday, Hamas freed 17 hostages, including 14 Israelis, and Israel released 39 Palestinian prisoners — the third such exchange under the truce.

Most hostages appeared to be physically well, but 84-year-old Elma Avraham was airlifted to Israel’s Soroka Medical Center in life-threatening condition because of inadequate care, the hospital said.

Avraham’s daughter, Tali Amano, said her mother was “hours from death” when she was brought to the hospital. Avraham is currently sedated and has a breathing tube, but Amano said she told her of a new great grandchild who was born while she was in captivity.

Avraham suffered from several chronic conditions that required regular medications but was stable before she was kidnapped, Amano said Monday.

So far, 19 people of other nationalities have been freed during the truce, mostly Thai nationals. Many Thais work in Israel, largely as farm laborers.

The Palestinian prisoners released were mostly teenagers accused of throwing stones and firebombs during confrontations with Israeli forces, or of less-serious offenses. Many Palestinians view prisoners held by Israel, including those implicated in attacks, as heroes resisting occupation.

The freed hostages have mostly stayed out of the public eye, but details of their captivity have started to trickle out.

Merav Raviv, whose three relatives were released Friday, said they had been fed irregularly and lost weight. One reported eating mainly bread and rice and sleeping on a makeshift bed of chairs pushed together. Hostages sometimes had to wait for hours to use the bathroom, she said.

More than 13,300 Palestinians have been killed since the war began, roughly two thirds of them women and minors, according to the Health Ministry in Hamas-ruled Gaza, which does not differentiate between civilians and combatants. More than 1,200 people have been killed on the Israeli side, mostly civilians killed in the initial attack. At least 77 soldiers have been killed in Israel’s ground offensive.

The calm from the truce allowed glimpses of the destruction wreaked by weeks of Israeli bombardment that leveled entire neighborhoods.