But shortly after the appeal by Ismail Haniyeh, Israeli troops opened fire on a car in the West Bank town of Bethlehem and killed four Palestinian militants, clouding the prospects for a cease-fire.
This violence comes after an earlier arrest raid in the West Bank Wednesday morning where Israeli troops killed an Islamic Jihad militant in a pre-dawn gun battle, according to Palestinians and the Israeli military.
CBS News correspondent Robert Berger reported that killing was a sign that thebetween Palestinian militants and Israel that had briefly kept the peace, was in jeopardy.
Among the conditions for an end to fighting that Haniyeh set earlier was a halt to Israeli military operations in the West Bank.
"We are talking about a mutual comprehensive calm, which means that the enemy must fulfill its obligations," Haniyeh said in a speech at Gaza City's Islamic University. "The Israelis must stop the aggression ... including assassinations and invasions, end the sanctions and open the borders."
Haniyeh's offer came amid signs that Israel and Hamas are moving closer to an Egyptian-brokered deal to end weeks of fighting that have killed more than 120 Palestinians and five Israelis.
Israel stepped up attacks on Gaza two weeks ago in response to repeated rocket barrages on southern Israeli towns by Hamas militants. The fighting has subsided in recent days. But both sides have denied talk of a formal truce and there are no direct contacts.
The U.S. fears continued fighting will torpedo peace talks between Israel and moderate Palestinian President Mahmoud Abbas, who controls a West Bank government that rivals Hamas' rule of Gaza.
Hamas does not recognize Israel's right to exist and is sworn to its destruction. Israel refuses to deal with the Hamas government.
But cutting a deal with Hamas would amount to international recognition of its control of Gaza. Israel and Abbas - who are involved in internationally backed peace talks - would essentially be agreeing to work with the militants instead of trying to topple them, allowing Hamas to stay in power while they try to negotiate a peace deal.
The deal could also give Abbas a new foothold in the area.
At the center of the arrangement would be deployment of officers loyal to Abbas at Gaza's border crossings with Israel and Egypt. Hamas officials said they accept such a deployment in principle, even though it means giving up some control. They said they have given Egypt names of pro-Abbas officers who would be acceptable to Hamas.
Haniyeh said "all of the factions are involved," signaling that Hamas' call for a halt to the fighting has the support of smaller militant groups that have often scuttled cease-fire attempts in the past.
Haniyeh used the word "tahdia," or calm, to describe the informal cease-fire he sought. He did not use the Arabic word "hudna," which is interpreted as a more formal truce. Both terms denote a temporary cease-fire rather than a permanent peace, but even the subtle differences between the words has led to fierce debate among Arabs in past cease-fire efforts.
Israel has repeatedly warned that Hamas would use any lull to rearm. And Israeli Defense Minister Ehud Barak made clear Wednesday that a cease-fire was not yet in place.
"We are not in a situation of an arrangement here," Barak said during a tour of the Gaza border. "We are in the midst of operations aimed at stopping rocket fire," he added. "There is no change in what we're doing. What awaits us here is more operations."
The remarks were followed by the Israeli West Bank attack. Palestinian security officials said one of the four killed was the commander of Islamic Jihad in the Bethlehem area, Mohammed Shehadeh, and two others were also members of Islamic Jihad. The fourth belonged to the Al Aqsa Martyrs Brigades, a violent offshoot of Abbas' Fatah.
Islamic Jihad leader Nafez Azzam in Gaza denounced the killings.
"This new crime reflects the true face of the occupation," he said. "Killing still continues while they are talking about the possibility of bringing calm. But if they think that calm means Palestinian surrender, they are mistaken."
While Haniyeh's demands were not new, the timing and location of the speech were significant. Haniyeh had been in hiding for several weeks during heavy fighting with Israel, and only has felt safe enough to appear in public in recent days.
With U.S. backing, Egypt has been trying to broker a truce.
"There are efforts by the Egyptian brothers who are working on this issue. We as Palestinians are waiting for the Israeli answers," Haniyeh said. "The ball is in Israel's court."
Hamas officials said they have proposed that security forces loyal to Abbas, their fierce rival, be allowed to monitor Gaza's border crossings.
"We have agreed to have the Palestinian Authority staff on the border, not our staff, as long as those involved in corruption be excluded," said Alaa Araj, an adviser to Haniyeh. "The details are being discussed in Cairo."
Allowing Abbas' men to guard the crossings would mark a significant concession by Hamas, which has ruled Gaza since violently ousting the presidents' forces last June. But it might be acceptable to Israel given its peace talks with Abbas.
Abbas has refused to speak to Hamas since the takeover, demanding it first relinquish power.
Israel and Abbas hope to reach a final peace agreement by the end of the year. But Israel has said it cannot carry out any deal until Abbas regains control of Gaza.
The Palestinians want an independent state that includes the West Bank and Gaza - areas located on opposite sides of Israel.