Prime Minister Ehud Olmert of Israel promised the Palestinian president, Mahmoud Abbas, on Sunday that Israel would no longer disrupt the supply of food, medicine and necessary energy into the Gaza Strip and intended to prevent a “humanitarian disaster” there.

Last Wednesday, the Hamas rulers of Gaza broke open the border to Egypt, allowing hundreds of thousands of Palestinians to seek goods that Israel had restricted in its clampdown on the region.

As an indication of the altered Israeli attitude, the government told the Supreme Court, which was meeting to hear a petition against Israeli efforts to cut electricity and fuel to Gaza, that industrial diesel fuel needed to run Gaza’s main power station would be supplied regularly, although in amounts that would not meet Gaza’s needs for uninterrupted electricity.

The court has not ruled, but the government also said that supplies of gasoline and regular diesel fuel to Gaza would be resumed, although in diminished amounts.

Mr. Olmert and Mr. Abbas met for two hours at the prime minister’s official residence here in one of their regular sessions on a peace treaty, then were joined by their chief negotiators, the Israeli foreign minister, Tzipi Livni, and the former Palestinian prime minister, Ahmed Qurei, who met privately afterward. But the leaders’ meeting, which officials of both sides described as cordial, was dominated by the crisis along the Gaza-Egyptian border.

Mr. Abbas wants his presidential guard to take over the Palestinian side of the crossings from Israel to Gaza and from Gaza to Egypt, but Israeli officials are skeptical, because of Hamas control of Gaza. They said control of the crossings was not a major topic on Sunday, because Mr. Abbas will travel to Egypt on Wednesday to discuss the issue with President Hosni Mubarak.

On a day of heavy rain in Gaza, Egyptian border police and troops again tried to increase order, restricting the passage of cars and trucks from Gaza and blocking the road from Rafah to the provincial capital, El Arish. Most of the traffic was Gaza-bound, but some Palestinian pedestrians continued to move into Egypt for a fifth day, blocking the muddy streets of Rafah but finding little left to buy.

It appeared that Egypt had decided to restrict the resupplying of goods to El Arish and Rafah to try to end the chaotic situation and re-establish control over the border. The mood was glum and angry, with witnesses reporting some fistfights between Palestinians and Egyptians.

Armed Hamas security men, some in uniform, patrolled the border, as if to show they could not be left out of any new border arrangement. Mr. Abbas, the leader of the Fatah faction, refuses to meet with Hamas. Mr. Mubarak will meet separately with the rival groups.

Foreign Minister Ahmed Aboul Gheit of Egypt met in Cairo with the appointed Palestinian prime minister based in Ramallah, Salam Fayyad, and said Egypt would soon take “necessary actions and measures” to control the border. Mr. Fayyad, an Abbas ally, wants the Palestinian Authority to be given control of the crossings and the Palestinian side of the border, with the supervision of European Union monitors, as it was before June, when Hamas routed Fatah to take control of Gaza.

But a senior Israeli official, who demanded anonymity because of the delicacy of the topic, said: “As far as we’re concerned it doesn’t seem to be such a strong idea, given the weakness of Abbas. And given that Hamas is there, one can assume it wouldn’t be too difficult for them to take de facto control.”

Mr. Olmert was not explicit on that point to Mr. Abbas, not wanting to offend him, the official said. And Mr. Olmert authorized more supplies to Gaza as a gesture to Mr. Abbas, the official said. But under the pressure of the Hamas breach of the Egyptian border, a popular move among Gazans, it could seem a hollow gesture.

Israeli has restricted supplies into Gaza, which it has labeled a “hostile entity,” to try to push Hamas to stop any militant group from firing into Israel. But the move backfired when Hamas breached the border, letting Gazans cross to buy supplies.

The Israeli statement to the court on Sunday was a kind of concession that the policy had failed, but it made clear that Israel wound continue restrictions to keep Gazans uncomfortable.

Sari Bashi, director of an Israeli advocacy group, Gisha, which was part of the court case, said, “This is part of a stop-start game that continually pushes Gazan residents to the brink, pushing them over, then pulling them back temporarily.” She said that “for the last seven months, Israel has been slowly reducing Gaza residents to desperation.”

Separately, as expected, the Israeli attorney general, Menachem Mazuz, said he would not indict police officers involved in the deaths of 13 Arab civilians in 10 days of Arab-Israeli demonstrations in October 2000. In a legal opinion, he upheld a decision by the Justice Ministry in September 2005 to close the investigation of the case.