For two hours in Jerusalem yesterday, Ehud Olmert and Mahmoud Abbas agonised over Hamas's demolition job on the Gaza-Egyptian border fence and the collapse of their joint strategy of isolating the Strip's Islamist rulers. But the Israeli Prime Minister and Palestinian President came up with no new answers.
Israel agreed to continue allowing humanitarian food and medical supplies to enter Gaza at the present rate of 50 lorries a day. It will also deliver about 500,000 litres of diesel oil and petrol a day for vehicles, industry and power stations after a 10-day embargo. This is enough to ward off a humanitarian crisis, but far short of meeting demand. Electricity is still being cut for hours every day.
But the summit did not address Mr Abbas's request for the Fatah-led Palestinian Authority to share control of the Rafah crossing with Egyptian and European monitors. Mr Abbas will discuss that with President Hosni Mubarak in Cairo on Wednesday. Egypt, which is trying to bring the two Palestinian sides together, is no longer even pretending to boycott Hamas.
Israeli officials doubt whether Mr Abbas's proposal will achieve anything. Shlomo Dror, a Defence Ministry spokesman, said: "As long as Hamas is determined to keep the crossing open, it will be very hard for either the Palestinian Authority or Egypt to close it. They don't have the power. Egypt is restricted to 750 armed police there. In the end, Hamas is going to control it."
But Mr Abbas's officials persisted in refusing to recognise the Hamas coup. Border control, they said, was a matter for Egypt, the Europeans, Israel and the Palestinian Authority. "There is no fifth party called Hamas," one said.
Hamas retorted that the old Rafah arrangement was a thing of the past. Sami Abu Zuhri, its spokesman, said: "If the Palestinian Authority does not want to meet Hamas in Cairo, we will discuss the border with Egypt alone."
Despite Egyptian attempts to reseal the border, hundreds of Palestinians continued surging into northern Sinai yesterday. Egyptian police prevented many of them going as far as the regional capital, El Arish, and limited the entry of cars.
One of the main complaints by Palestinians in Gaza City was that businessmen were profiteering from cheap goods smuggled from Egypt.