Indirect talks over a long-term solution for Gaza began in Cairo on Tuesday.
The talks, between Israel and a Palestinian delegation including members of Hamas and Islamic Jihad, broke up on Wednesday for Rosh Hashanah and are scheduled to resume next week. The Palestinians remained in Egypt to discuss the unity agreement.
In recent days, Hamas has downplayed previous threats to renew attacks on Israel.
The inclusion of their senior leaders Mussa Abu Marzouk and Mahmoud a-Zahar in the Cairo talks is seen as an indication that they are serious about pursuing a long-term deal.
The negotiations will be carried out through Egyptian mediators. They follow an interim deal signed last week to allow building materials into Gaza under international supervision.
The opening positions of the sides were extremely far from each other, with Israel demanding disarmament of the military groups in Gaza as a condition for any significant opening of the Strip. Hamas, meanwhile, is refusing to relinquish its rocket arsenal and demanding that Israel allow them to build an airport and a seaport.
The one area of possible agreement is the plan for PA security personnel to be deployed in the Strip, perhaps alongside international peacekeepers. This would allow land crossings into Israel and Egypt to be opened up, both for travel and commerce.
It is unclear at this stage whether the negotiations will include talks over the repatriation of body parts of two IDF soldiers killed in Gaza, Hadar Goldin and Oron Shaul.
Officially, the talks between the Palestinian factions on the implementation of the unity agreement signed four months ago are not connected to the Gaza situation. However, the unity talks are expected to be key to any deal with Israel as the PA has been so far reluctant to redeploy its forces in Gaza without additional assurances from Hamas that they will not be harmed.
Palestinian President Mahmoud Abbas is hoping that Hamas will endorse his diplomatic plan for renewed talks with Israel on the basis of a clear timetable for the establishment of a Palestinian state.