A Gaza Truce Aids Both Israel and Hamas. Until the Calculus Changes.

The decision by Israel and Hamas to extend their brief truce has created short-term benefits for both sides but amplified uncertainty about how, when and whether Israel will continue its invasion of the Gaza Strip.

The agreement to prolong the cease-fire to six days from four has raised expectations that both sides will now agree to more short extensions — but if that happens, it may only increase the competing pressures on Israel.

From the outside world, Israeli leaders will face calls to make the cease-fire permanent. Within their own country, however, there will be competing demands that they resume fighting and crush Hamas, while also securing the release of Israeli hostages.

On Tuesday, both Israel and Hamas accused each other of violating the truce. The Israeli military said that explosive devices had been detonated near its troops in two places in northern Gaza, and that militants in one area had fired on them. Hamas said its fighters had engaged in a “field clash” provoked by Israel, without offering additional details.

But neither side signaled that it was pulling out of the agreement, and on Tuesday, Hamas released 12 more hostages — 10 Israelis and two 2 Thai nationals — who were kidnapped when it attacked Israel on Oct. 7. Another release is expected on Wednesday.

Since the pause in fighting began on Friday, Hamas has returned 60 Israeli hostages and through separate negotiations has released 21 citizens of other countries. Israel has freed 180 Palestinians held in its prisons.

For the moment, the small extensions of the cease-fire are serving both Hamas and Israel.

For Hamas, they allow the organization to prolong its control of most of Gaza, where it has been routed in much of the north by Israeli forces. A longer pause would give Hamas more time to regroup and reposition its forces.

For Israel, each extension means the return of still more of its citizens taken captive by Hamas — welcome news for a public that was traumatized by the raids and is following developments in Gaza closely. Roughly 240 people were taken hostage by Hamas and its allies, and for every extra day of the cease-fire, the two sides have agreed to exchange roughly 10 Israelis for 30 Palestinians jailed in Israel.

Gazans also benefit from the cease-fire, which has allowed more aid to be delivered through Egypt to its 2.2 million residents, most of whom have been uprooted by the fighting and face profound food and fuel shortages.

But the longer the dynamic lasts, the greater Israel’s conundrum.

With each day’s release of Palestinians held in Israeli jails, Hamas’s popularity in the Israeli-occupied West Bank, where many of the freed Palestinians have returned, has surged. That could add fuel to a low-level conflict there.

A long pause in the fighting in Gaza may also slow Israel’s invasion, putting at risk its stated goal of removing Hamas from power. Already, Biden administration officials are pushing Israel to fight more surgically once it returns to its invasion. And international pressure is building on Israel to stop its attacks entirely.

At home, some Israelis fear that a prolonged extension would give Hamas too much power over the Israeli psyche, said Anshel Pfeffer, a political commentator for Haaretz, a left-leaning Israeli newspaper.

“Israel faces a real dilemma,” said Mr. Pfeffer. “With each hostage release, Hamas holds the whip hand over Israeli emotions. Ultimately, Israel will have to decide between freeing more hostages — or preventing Hamas from dictating the mood of the country.”

The capture of so many hostages, among them a 9-month-old baby, has taken a heavy toll on many Israelis, and the complicated hostage negotiation process, fraught by delays and disagreements, has only heightened that torment.

The mediators who worked to bring about the cease-fire are hoping that the current model will generate enough momentum to prevent the resumption of hostilities and create the conditions needed for longer-term discussions to take place, two people with knowledge of the mediation efforts said, who spoke on condition of anonymity to discuss sensitive negotiations.

But they expect the process to get more difficult if all the civilian hostages are out and the negotiations move to the release of Israeli soldiers who were seized on Oct. 7. Hamas is expected to demand the release of either more detainees from Israel or higher-profile ones — a change in “the exchange rate,” as one person with knowledge of the talks put it.

On Tuesday, the director of the Central Intelligence Agency, William J. Burns, arrived in Doha, Qatar, for a new round of negotiations aimed at freeing more hostages held in Gaza, according to U.S. officials. Mr. Burns and David Barnea, the head of the Mossad, Israel’s spy service, met with Abbas Kamel, the head of Egypt’s intelligence service, and Mohammed bin Abdulrahman bin Jassim al-Thani, the prime minister of Qatar.

Israeli Defense Force officials say they remain determined to wipe out Hamas, which killed an estimated 1,200 people when it attacked on Oct. 7. More than 13,000 people have been reported killed in Gaza in the Israeli air and ground assault that followed.

“The I.D.F. is prepared to continue fighting,” Israel’s military chief of staff, Herzi Halevi, said in a statement on Tuesday. “We are using the days of the pause as part of the framework to learn, strengthen our readiness and approve future operational plans.”

Israel has said it is targeting Hamas all over Gaza, including in places its members are embedded among civilians, and in an extensive tunnel network underground.

Israeli troops have captured a swath of northern Gaza roughly in the shape of a C: the northern edge of the strip, a sliver along the Mediterranean coast, and the central strip below Gaza City. The forces largely encircled Gaza City and split the strip in two halves, seeking to disrupt Hamas’s grip over the enclave and begin ousting it from its biggest city.

Some analysts say Israeli domestic pressures will probably prompt Prime Minister Benjamin Netanyahu to revive the invasion sooner rather than later. Delaying it would put Mr. Netanyahu on a collision course with far-right government ministers who grudgingly supported the cease-fire because they were assured that the invasion would continue after only a short truce.

Ben Hubbard contributed reporting.