JERUSALEM AND CAIRO — After 19 days under Israeli military assault and Egyptian diplomatic pressure, Hamas on Wednesday softened its terms for a cease-fire as fighting in the Gaza Strip pushed the death toll past 1,000.
The Palestinian militant group altered its stance in talks with Egyptian mediators in Cairo. It was the first sign of progress toward a deal to end the punishing offensive and halt rocket fire from Gaza into southern Israel.
Israel announced that it would send an emissary, Defense Ministry official Amos Gilad, to Cairo today to discuss a cease-fire proposal with officials there.
Fighting in Gaza took another gruesome turn Wednesday. An Israeli airstrike hit a cemetery, shattering headstones and scattering body parts and decaying flesh. Militants in Lebanon provoked an exchange of rocket fire with the Israeli army for the second time in a week, threatening to widen the conflict.
Israel and Hamas were seeking a way out. Hamas' 15,000-man paramilitary force, although still dangerous, has been badly weakened. Israeli officials believe they are close to achieving the goal of the offensive: stopping years of rocket fire from Gaza.
Hamas had previously demanded that Israel halt the offensive, pull its forces from Gaza and lift a crippling blockade of the 140-square-mile territory as a precondition for a cease-fire.
On Wednesday, the group offered a temporary truce that would give Israel five days to withdraw while talks continue on two underlying issues: Hamas' insistence on open borders and Israel's demand for a halt to the smuggling of rocket components and other weapons through tunnels from Egypt into Gaza.
A senior Hamas official in Cairo disclosed the group's new position on condition of anonymity after Egyptian and Hamas officials decided not to comment publicly on the talks.
Hamas altered its terms after Egypt reportedly pressed for a 10-day temporary truce. Israel's air and ground attack also apparently swayed Hamas' leaders in Gaza, who in recent days sounded more open to a deal than did their exiled counterparts in Syria.
Egypt is overseeing the cease-fire talks in part because Israel refuses to negotiate directly with Hamas, which it considers a terrorist organization.
At the same time, Israel is trying to persuade Egypt to accept international assistance in patrolling its side of the border with Gaza to prevent weapons smuggling. A senior Israeli Foreign Ministry official headed to Washington today for talks with U.S. officials on a plan to help Egypt secure the border.
Israeli officials have insisted that they will not halt the offensive until Egypt puts an anti-smuggling mechanism in place. But Israel's position was unclear Wednesday after Defense Minister Ehud Barak suggested a weeklong "humanitarian" cease-fire, only to be reprimanded by other officials for airing proposals in public.
Even if a truce is achieved soon, it would probably take more than a few days to resolve the issues of Gaza's borders.
Hamas demands that Israel and Egypt open Gaza's border crossings to commerce, fuel and human passage. Both countries have tightened a blockade since Hamas, which calls for Israel's destruction and has close ties to Islamic foes of Egypt's government, seized control of Gaza in 2007 from the more moderate Fatah faction that now runs the West Bank-based Palestinian Authority.
Israel has been reluctant to tie a cease-fire deal to a reopening of its border crossings. And Egypt insists that its border with Gaza can be open only if the European Union and the Palestinian Authority place monitors inside Gaza, a condition Hamas rejects.
United Nations Secretary-General Ban Ki-moon arrived in the region Wednesday to press the U.N. Security Council's call last week for an immediate and "durable" cease-fire. International criticism of Israel has mounted, with Bolivia breaking off diplomatic relations.
"It is intolerable that civilians bear the brunt of this conflict," Ban said in Cairo after meeting Egyptian President Hosni Mubarak.
An Israeli coalition of eight human rights groups issued the same message, directed at Israel. It said the military offensive had put Gaza's 1.5 million residents "in extreme humanitarian distress."
The coalition urged Israel to stop targeting civilian areas, open routes for civilians to escape battle zones and allow for the restoration of normal medical care, electricity, water and other essential services.
Col. Moshe Levy, commander of the Defense Ministry's Gaza Liaison Office, denied there was a humanitarian crisis. He said Israel had allowed more than 1,000 truckloads of food, medical supplies and other aid to enter Gaza since the offensive began Dec. 27. He said he suspected Hamas fighters were stealing some of the aid.
Military officials have set up a special operations center in Tel Aviv to help improve aid groups' delivery of emergency supplies to Gaza.