The soldier whose abduction sparked Israel's invasion of Gaza is alive and in stable condition, a Palestinian official said Saturday, and President Mahmoud Abbas warned that the coming hours were "critical, sensitive and serious" for resolving the crisis.

Israeli soldiers and Palestinian militants exchanged fire for several hours Saturday afternoon when Israeli tanks and bulldozers crossed the border with Gaza and began razing farmland east of the town of Khan Younis.

Militants shot an anti-tank rocket at one of the vehicles. The army responded with gunfire and a missile launched from an unmanned plane. No major injuries were reported on either side.

The fighting took place north of the position Israeli troops have occupied since they entered Gaza on Wednesday. The army said it was carrying out a limited operation in the area and the soldiers were expected to leave soon.

There has been no sign of Cpl. Gilad Shalit, 19, since he was abducted a week ago during a militant raid on an Israeli army post just outside Gaza that killed two soldiers and two of the attackers.

The Hamas-affiliated militants holding Shalit initially said they would trade information about him for all Palestinian women and underage prisoners being held in Israeli jails. The militants raised their demands Saturday, calling for an end to the Israeli offensive and the release of 1,000 additional prisoners held by Israel, including non-Palestinian Muslims and Arabs.

The new demand appeared aimed at rallying support in the Arab world.

Israel has ruled out any compromise with the kidnappers, saying it would only encourage more abductions.

Ziad Abu Aen, a Palestinian deputy minister and a Hamas official, said "mediators" told him Shalit had received medical treatment for the wounds he sustained in the raid and was in stable condition.

"He has three wounds," Abu Aen said in the West Bank city of Ramallah. "I guess shrapnel wounds."

Egypt and other foreign mediators have been working to try to resolve the crisis, but Abbas said those efforts had yet to bear fruit mainly because it was unclear who in Hamas — the militants or the group's leadership abroad — was authorized to make decisions about Shalit's fate. Prime Minister Ismail Haniyeh, also a Hamas leader, apparently has no say in the matter, according to a statement from Abbas' office.

"The next hours are critical, sensitive and serious. And though the efforts are still ongoing, we have not reached an acceptable solution until now," Abbas' office said in a separate statement.

Prime Minister Recep Tayyip Erdogan of Turkey, a predominantly Muslim country that has close ties with Israel, called President Bush on Saturday and talked for 30 minutes about the crisis.

"The president said that the initial goal should be freeing the Israeli soldier — that is the key to ending the crisis," said Frederick Jones, spokesman for the National Security Council at the White House.

Meanwhile, the fuel supply in Gaza began dwindling after Israel cut off the flow through a pipeline. Gas stations across the territory ran dry, and human rights groups worried that if fuel shipments were not restored in the coming days, Gaza could face a humanitarian crisis as generators used to pump water and power hospitals stopped working.

"We have enough to last between three to seven days. If we don't get a new supply, it will be an environmental disaster," said Eissa Daher, acting mayor of the town of Jebaliya.

Authorities have been relying on generators since an Israeli airstrike Tuesday destroyed Gaza's only power plant, knocking out 43 percent of the territory's electricity supply, the United Nations said. The remaining electricity comes from Israel.

The Israeli army said Israel had increased the supply of electricity to Gaza to make up for the power shortage and would work to allow food and fuel to enter in the coming days.

In addition to the fighting near Khan Younis, Israel kept up the military pressure, with aircraft and gunboats pounding open ground in Gaza that the army said militants were using to launch homemade rockets into Israel.

One airstrike hit a greenhouse left behind when Israel pulled out of Gaza last summer after 38 years of occupation, damaging what had once been a symbol of hope for Gaza's economic rebirth.

Although troops remained massed on the border, Israel on Thursday postponed a planned invasion of northern Gaza as international mediators sought a way out of the crisis. But with no apparent progress on the diplomatic front, it was unclear how much longer they would hold off.