But with the sides' demands still seemingly irreconcilable, that optimism may be premature and a deal not so close in the making.
Israel and Hamas are observing a five-day cease-fire which began at midnight Wednesday, in an attempt to allow talks between the sides in Cairo to continue. The negotiations are meant to secure a substantive end to the monthlong war and draw up a roadmap for the coastal territory, which has been hard-hit in the fighting.
Israeli officials have largely kept quiet about the negotiations. But militant groups represented in Cairo said progress was being made toward a deal - a stark turnaround from earlier posturing.
"The war is now behind us, and the chances for an agreement on a lasting cease-fire are encouraging," Ziad al-Nakhaleh, deputy leader of the Islamic Jihad militant group, told The Associated Press. "Though we didn't get all that we wanted, there was progress here and there."
Israeli government spokesman Mark Regev would not comment Thursday on the Cairo talks.
Beyond demands for a seaport and airport, Hamas is also seeking an end to a crippling blockade imposed by Israel and Egypt in 2007, when Hamas seized control of the coastal strip. 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, meanwhile, is demanding that Hamas be disarmed, or at the very least, be prevented from re-arming, a term that is a virtual non-starter for the militant group.
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.
The sides are studying an Egyptian proposal which calls for easing parts of the Israeli blockade of Gaza, bringing some relief to the territory.
But the proposal leaves the key areas of disagreement, including Hamas' demand for a full lifting of the blockade and Israeli calls for Hamas to disarm, to later negotiations.
On Wednesday, as the head of the Palestinian delegation Azzam al-Ahmad announced the cease-fire had been extended for an additional five days, he also noted that there had been "significant progress." But, highlighting the devil-in-the-details nature of the negotiations, he also said disagreements remained over wording regarding security arrangements, reconstruction efforts for the Gaza Strip and the permissible fishing area.
"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 said.
Al-Haya 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.
While the cease-fire was largely holding, it got off to a rocky start, highlighting the fragility of the talks and the risk of slipping back into conflict.
Violence briefly spiked as the extension of a previous, 72-hour truce was announced shortly before midnight on Wednesday. The extension is to last until midnight on Monday.
Israel's military said eight 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.
The current cease-fire is the longest to be declared since the war broke out last month in the Gaza Strip. The fighting has so far killed more than 1,900 Palestinians, the majority of them civilians, according to Palestinian and U.N. officials. Israel has lost 67 people, all but three of them soldiers.
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 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.
Goldenberg reported from Jerusalem. Associated Press writer Peter Enav in Jerusalem contributed to this report.