Israel says it will resume regular fuel supplies to Gaza in a week's time. They were stopped 10 days ago due to rocket attacks by Palestinian militants.
Hamas militants have been manning the border
The decision was announced at a Supreme Court hearing brought by human rights groups against the blockade.
It came as the Israeli and Palestinian leaders met for the first time since a crisis on the Gaza-Egypt border began.
Hamas militants blew holes in the border five days ago, leading thousands of Palestinians to cross unhindered.
Egyptian police have tried, unsuccessfully, to reseal the breaches.
Egypt has asked the militants to attend talks "promptly" on the crisis.
Hearings and talks
At Sunday's hearing, the Israeli government promised to resume supplies of fuel, but not at normal levels, in a week's time.
A total of 2.2m litres a week will be allowed through, the minimum to keep Gaza's power station in operation.
Palestinian Authority President Mr Abbas discussed the crisis with Israeli Prime Minister Ehud Olmert during their meeting on Sunday.
He renewed his offer to take control of Gaza's border crossings instead of Hamas, but received no official Israeli response.
However, both leaders spoke at length about "the need to prevent a humanitarian crisis in the Gaza Strip," Mr Olmert's spokesman David Baker said.
The two are engaged in a new US-backed peace process that has excluded - and is rejected by - Hamas.
What Israel didn't want, says the BBC's Aleem Maqbool in Jerusalem, was for the Palestinian president to talk to Hamas, which controls Gaza.
However, our correspondent adds that as the Egyptians have already discovered, closing the border without the consent of Hamas is likely to be extremely difficult.
Mr Olmert and Mr Abbas resolved to talk again after the Palestinian leader meets his Egyptian counterpart, Hosni Mubarak, on Wednesday.
Reluctance to talk
Egypt has been reluctant to talk to Hamas since June when the Islamist group seized control of Gaza, ousting Mr Abbas's Fatah faction, the BBC's Heba Saleh reports from Cairo.
Egypt wants to restore arrangements on the border to their state before Hamas took control of Gaza.
Before June the border was under the control of the Palestinian Authority but traffic through it was supervised by European monitors.
17 January: Israel seals border following rise in rocket attacks
20 January: Gaza's only power plant shuts down
22 January: Israel eases restrictions
22 January: Egyptian border guards disperse Palestinian protest against closure
23 January: Border wall breached