Egyptian President Mohammed Morsi said the negotiations between the two sides would yield "positive results" during the coming hours.
Israel demands an end to rocket fire from Gaza and a halt to weapons smuggling into Gaza through tunnels under the border with Egypt. It also wants international guarantees that Hamas will not rearm or use Egypt's Sinai region, which abuts both Gaza and southern Israel, to attack Israelis.
Hamas wants Israel to halt all attacks on Gaza and lift tight restrictions on trade and movement in and out of the territory that have been in place since Hamas seized Gaza by force in 2007. Israel has rejected such demands in the past.
In Brussels, a senior official of the European Union's foreign service said a cease-fire would include an end of Israeli airstrikes and targeted killings in Gaza, the opening of Gaza crossing points and an end to rocket attacks on Israel. The official spoke on condition of anonymity because he was not authorized to speak to the media.
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. The men 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 it served as a Hamas communications post.
By Tuesday, 133 Palestinians, including at least 54 civilians, were killed since Israel began an air onslaught that has so far included nearly 1,500 strikes. Some 840 people have been wounded, including 225 children, Gaza health officials said.
Five Israelis, including an 18-year-old soldier and a civilian contractor who worked for the military struck by rocket fire Tuesday, have also been killed and dozens wounded since the fighting began last week, the numbers possibly kept down by a rocket-defense system that Israel developed with U.S. funding. More than 1,000 rockets have been fired at Israel this week, the military said.