Morsi belongs to the Muslim Brotherhood, Hamas' parent movement, and clearly sympathizes with the Islamic militant group. At the same time, he relies heavily on U.S. aid and is trying to preserve a historic peace agreement with Israel.
Earlier, Morsi raised hopes that a cease-fire was near when he predicted the negotiations would yield "positive results" during the coming hours.
Netanyahu also said his country would be a "willing partner" in a cease-fire agreement.
But as the talks stretched into the evening, it became clear that a deal remained a ways off.
"Most likely the deal will be struck tomorrow. Israel has not responded to some demands, which delayed the deal," Hamas official Izzat Risheq said.
Hamas officials refused to discuss the remaining sticking points.
Israeli media quoted Defense Minister Ehud Barak as telling a closed meeting that Israel wanted a 24-hour test period of no rocket fire to see if Hamas could enforce a truce.
Palestinian officials briefed on the negotiations said Hamas wanted assurances of a comprehensive deal that included new border arrangements — and were resisting Israeli proposals for a phased agreement. The officials spoke on condition of anonymity because they were not authorized to talk to the media.
Although Israel claims it has inflicted heavy damage on militants' capabilities, its roughly 1,550 airstrikes and shelling attacks have failed to halt the rocket fire.
More than 1,400 rockets have been fired at Israel, including about 200 on Tuesday. A U.S.-financed Israeli rocket-defense system has knocked down roughly 400 of the incoming projectiles.
Violence raged on as the talks continued. An airstrike late Tuesday killed two journalists who work for the Hamas TV station, Al-Aqsa, according to a statement from the channel. A third journalist, from Al Quds Educational Radio, a private station, also was killed.
The Al-Aqsa TV cameramen were in a car hit by an airstrike, Gaza health official Ashraf al-Kidra said. Israel claims that many Hamas journalists are involved in militant activities. Earlier this week it targeted the station's offices, saying they served as a Hamas communications post.
Late Tuesday, a Palestinian rocket hit a house in the central Israeli city of Rishon Lezion, wounding two people and badly damaging the top two floors of the building, police spokesman Micky Rosenfeld said.
Minutes before Ban's arrival in Jerusalem from Egypt, Palestinian militants fired a rocket toward Jerusalem, just the second time it has targeted the city. The rocket fell in an open area southeast of the city.
Jerusalem had previously been considered beyond the range of Gaza rockets — and an unlikely target because it is home to the Al-Aqsa Mosque compound, Islam's third-holiest shrine.
Israeli warplanes dropped leaflets on several Gaza neighborhoods asking residents to evacuate and head toward the center of Gaza City along specific roads. The army "is not targeting any of you, and doesn't want to harm you or your families," the leaflets said. Palestinian militants urged residents to ignore the warnings, calling them "psychological warfare."
Israeli security officials acknowledge they rely on a network of Palestinian informants to identify targets. Masked gunmen publicly shot dead six suspected collaborators with Israel in a large Gaza City intersection Tuesday, witnesses said.
An Associated Press reporter saw a mob surrounding five of the bloodied corpses shortly after the killing, and one of the bodies was dragged through the streets by a motorcycle.
Hamas did not provide any evidence against the alleged collaborators.
Clinton was also scheduled to meet with Palestinian President Mahmoud Abbas in the West Bank and Egyptian leaders in Cairo on Wednesday. Turkey's foreign minister and a delegation of Arab League foreign ministers traveled to Gaza on a separate truce mission. Airstrikes continued to hit Gaza even as they entered the territory.
"Turkey is standing by you," Turkish Foreign Minister Ahmet Davutoglu told the Hamas prime minister in Gaza, Ismail Haniyeh. "Our demand is clear. Israel should end its aggression immediately and lift the inhumane blockade imposed on Gaza."
The U.S. considers Hamas, which has killed hundreds of Israelis in suicide and other attacks, to be a terror group and does not meet with its officials. The Obama administration blames Hamas for the latest eruption of violence and says Israel has the right to defend itself. At the same time, it has warned against a ground invasion, saying it could send casualties spiraling.
Barzak reported from Gaza City, Gaza Strip. Associated Press writers Hamza Hendawi in Cairo, and Karin Laub in Gaza City contributed to this report.
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