Israel's military said eight Hamas rockets were launched at Israel but that the firing stopped early Thursday morning. Israel retaliated with airstrikes on rockets and rocket-launching sites in Gaza, the military said.
Gaza police said 17 Israeli strikes were carried out, but that no one was killed or wounded.
Palestinian negotiators in Cairo expressed optimism that an agreement on a sustainable roadmap for the war-torn territory could soon be achieved.
"There is a real opportunity to reach an agreement, but (Israel) must stop the maneuvers and playing with words," said senior Hamas negotiator Khalil al-Haya, without elaborating.
"We are not interested in more destruction for our people. We are not interested in more bloodshed," he added.
Ziad al-Nakhaleh, the deputy leader of the Islamic Jihad militant group, told The Associated Press that he was confident a satisfactory agreement would be reached.
"The war is now behind us and the chances for an agreement on a lasting cease-fire are encouraging," al-Nakhaleh said in Cairo before leaving to Beirut to brief the group's leader, Ramadan Shallah, on the talks. "I believe we are heading toward an agreement," he said.
Hamas is seeking an end to a crippling blockade imposed by Israel and Egypt in 2007. The blockade has greatly limited the movement of Palestinians in and out of the territory of 1.8 million people. It has also restricted the flow of goods into Gaza and blocked virtually all exports.
Israel says the closure is necessary to prevent arms smuggling, and officials are reluctant to make any concessions that would allow Hamas to declare victory.
Israel wants Hamas to disarm, or at least be prevented from re-arming. Hamas has recovered from previous rounds of violence with Israel, including a major three-week air and ground operation in January 2009 and another weeklong air offensive in 2012. It still has an arsenal of several thousand rockets, some with long ranges and relatively heavy payloads.
Al-Haya, the Hamas negotiator, told reporters in Cairo that Hamas would seek international guarantees to enforce any agreements reached with Israel. He said that together with the Palestinian Authority, which runs the West Bank and with which Hamas formed a unity government earlier this year, the militant group would expect to play an important role in rebuilding Gaza.
The "national unity government is required to carry out its duty with regard to reconstruction," he said.
Early Thursday afternoon, Hamas negotiators flew from Cairo to Doha for consultations with Hamas leaders in Qatar.
It was the first time that Hamas figures were allowed to fly directly from the Cairo airport since a military-backed government took over in Egypt last year, replacing an Islamist president whose Muslim Brotherhood group was closely allied with Hamas. That appeared to reflect a recognition on Egypt's part of Qatar's importance in the talks.
Egypt has positioned itself as the key mediator, but its tough anti-Hamas policies could limit its effectiveness. The tiny Gulf Arab nation of Qatar is seen as a conduit for Hamas demands. It hosts several senior Hamas leaders and has staunchly opposed the Egypt-Israel blockade of the Palestinian coastal strip.
Israeli government spokesman Mark Regev would not comment Thursday on the progress of the Cairo talks.