JERUSALEM (CNN) -- Israeli officials Sunday expressed hope that Egypt will regain control of its border crossing with Gaza as the flow of Palestinians slowed to a trickle due to heavy rains and muddy roads.
Palestinians transport goods they bought in Egypt back into Gaza, after they crossed the Rafah border.
But Israel won't raise its concerns about the border breach with the Palestinian leadership until after President Mahmoud Abbas discusses the issue with Egyptian leaders later this week in Cairo.
The issue "did not come up at length" during Sunday's meeting between Abbas and Israeli Prime Minister Ehud Olmert in Jerusalem, Olmert's spokesman David Baker said.
The two leaders did address the current humanitarian situation in Gaza in what Baker described as "a constructive and helpful meeting."
Since the border was overrun last week, tens of thousands of Palestinians have streamed into Egypt to buy supplies and get medical attention unavailable inside Gaza because of Israel's clampdown on its borders.
Speaking at Sunday's weekly Cabinet meeting, Israeli Defense Minister Ehud Barak said Israel will continue to keep its border crossings with Gaza closed "while maintaining the humanitarian minimum required to maintain the civilian population in Gaza."
"We will not allow a humanitarian crisis in Gaza," Barak said in the closed-door meeting, according to his office.
That assertion got some support Sunday, when the Israeli state attorney to the Israeli High Court said that, beginning next week, Israel will allow shipments of fuel into Gaza, "in accordance with at least the humanitarian minimum" or no less than 75,400 liters per week.
Another 800,000 liters per week of diesel fuel was to be allowed for transportation. In addition, 2.2 million liters would be allowed for Gaza's power station.
Sunday's meeting between Abbas and Olmert was one of a series of ongoing talks held every two weeks as part of an agreement reached during November's Annapolis Mideast peace conference.
Abbas heads to Cairo on Wednesday to discuss last week's breach of the border by Palestinians in Gaza, which was undertaken with the approval of Gaza's Hamas leadership.
It was unclear if Hamas leaders have been invited to participate in the Cairo talks, which will include Egyptian President Hosni Mubarak.
Both Baker and Israeli Foreign Ministry Spokesman Aryeh Mekel said Israel's concerns about the Gaza-Egypt border situation would be addressed in depth with the Palestinian president after he returns from Egypt.
"Abu Mazen (Abbas) is going to Cairo and he will discuss this entire issue with President Mubarak and only afterwards will it be possible to continue these discussions between Israel and himself," Mekel said.
He stressed Israel's position that "it is the responsibility of Egypt" to take care of the situation.
"They have to find a way to close this border crossing and I believe they will," Baker said. "First of all, it is in their interests not to have Hamas terrorists roaming around the Sinai.
"Secondly, Egypt is known as a country that lives up to its agreements and commitments, and I believe they will do so in this case as well."
During Sunday's Cabinet meeting, Barak too voiced optimism that Egypt would regain control of the Rafah border crossing.
"(Egypt's) intention is to close the border and I assess that it will take a certain amount of time," the Israeli defense minister said.
Along the Gaza-Egypt border, Palestinians bulldozed a makeshift dirt road on Saturday to make it wider for cars to travel, but heavy rains on Sunday turned it into a muddied mess.
The road was packed with cars going into Egypt shortly after it was constructed, but there was little traffic a day later because of the dangerous conditions.
The main wall separating Egypt and Gaza that was partially destroyed by the Palestinians last week is still unrepaired, allowing for free access into and out of Gaza.
Egyptian troops are stationed across parts of the breached border wall, but are outnumbered and cannot stop the flow of Palestinians, many of whom have no plans to return to Gaza.
"If Egypt closes the border, we will find another way in, even if we have to come in by sea," said Yousif, a Gaza resident.
Roadblocks have been erected, and Egyptian forces are pushing the Palestinians to return without using a heavy hand.
The Rafah border crossing is supposed to be jointly maintained by Egypt and the Palestinian Authority -- led by Abbas -- under the oversight of the European Union monitors, but has been closed since Hamas took over Gaza and split with the PA leadership last year.
Hamas effectively controls the border now, and will continue to in the future, a senior Hamas adviser in Gaza told CNN's Ben Wedeman.
"When we decide to open it, (we) open it, when we decide to close it, (we) close it -- us and the Egyptians," Ahmed Yusif said.
Yusif is a senior adviser to former Palestinian Prime Minister Ismail Haniya, the Hamas official who is the de facto leader of Gaza.
"It shouldn't be the Israelis ... involved, or the Europeans, because it's the Egyptian security. Israel has nothing to do when it comes to the security with that gate." E-mail to a friend
CNN's Aneesh Raman in Al-Arish, Egypt contributed to this report.