Later on Sunday, Mr. Netanyahu told a group of workers for the Shin Bet, the country’s internal security agency, that Israel’s campaign in Iran had “opened up many opportunities, first among them to rescue the hostages.” Israel still must “resolve the Gaza issue and defeat Hamas,” he said, adding, “I believe that we will succeed in both these missions.”

In an unusual move, a panel of three Israeli judges agreed on Sunday to delay Mr. Netanyahu’s scheduled testimony by a week. The move was announced after the prime minister attended a special court hearing, behind closed doors and accompanied by two of Israel’s security chiefs, to press for a postponement of his upcoming court appearances.

The court has been cross-examining Mr. Netanyahu this month in two scheduled court appearances each week. Mr. Netanyahu has argued for a delay in his cross-examination based on national security imperatives, the details of which he has not publicly disclosed.

In recent days, the judicial authorities had rejected Mr. Netanyahu’s requests for a two-week postponement, saying the reasons he had provided were too general and unconvincing. It was not immediately clear what changed their minds. In the decision on Sunday, the judges said they would also consider Mr. Netanyahu’s request to delay his testimony for a second week, based on developments.

Mr. Trump had suggested on Friday that there could be an agreement between Israel and Hamas within a week. But Mr. Trump has offered no details on what may have changed, and analysts said it was unclear what his claim was based on.

There has been no advancement in the cease-fire talks, according to an Israeli official and another person familiar with the matter.

Israel and Hamas do not negotiate directly. But no Israeli negotiating teams have been dispatched to mediating countries, such as Qatar and Egypt — a sign that the two sides remain far apart, at least on the contours of the type of two-phased deal that has been discussed so far through the traditional channels. Still, it is possible that higher level discussions might be happening separately and in secrecy.

It was not immediately clear how many people might be affected by Sunday’s evacuation orders from the Israeli military. Gaza City and other areas in the northern part of the enclave were largely emptied earlier in the war following previous evacuation orders. But hundreds of thousands of residents of northern Gaza returned home during a two-month cease-fire, which collapsed when Israel resumed fighting in mid-March.

Negotiations since then for a renewed cease-fire have been at an impasse. Israel says it has accepted various versions of a proposal put forward by Steve Witkoff, the White House special envoy, which calls for a roughly two-month cease-fire and the release of about half the living hostages, along with the remains of some others. Talks for a permanent cease-fire would take place during that period, but the longstanding sticking points appear to remain unresolved.

Hamas says it will only release all the hostages in return for a full Israeli withdrawal from Gaza and an internationally guaranteed end of the war.

Israel has said the war can only end if Hamas’s surrenders and disarms, and it has demanded that the group’s leaders go into exile. Hamas has rejected those conditions.

The Hamas-led attack on Israel in October 2023 killed about 1,200 people, the majority of them civilians, according to the Israeli authorities. Israel’s counter offensive has killed more than 56,000 people in Gaza, according to the Gaza health ministry, which does not distinguish between combatants and civilians in its data but has said more than half of the dead are women and children.