Smoke rises from a Gaza neighbourhood during Israel's offensive against Hamas in the strip.
Hamas officials in Cairo have proposed a year-long truce with Israel and an opening of the crossings into the Gaza Strip, in the latest round of diplomatic meetings to build on a fragile ceasefire in the Gaza Strip.
Hamas official Ayman Taha told reporters in Cairo on Sunday that his delegation was briefed by the Egyptians on an Israeli proposal for a year-and-a-half long truce with only partial opening of the border, which they rejected.
Instead, Taha says the group made a counter offer of a year with open borders, which they now must discuss with their leadership in Damascus.
"We will study the matter again and it will be brought back to the Egyptians," he told MENA, the official Egyptian news agency, without elaborating on the other provisions of the possible deal.
Hamas has said in the past that it would only maintain a truce if Israel ended its blockade of the Gaza Strip and opened the crossings.
Israel's top negotiator on Gaza, Amos Gilad, was also in Cairo on Thursday for talks.
Israel and Hamas are engaged in indirect talks to build on a fragile ceasefire in the Gaza Strip after a 22-day Israeli assault to end Hamas rocket fire, which killed some 1,300 Palestinians.
The Hamas discussions with Egyptian intelligence chief Omar Suleiman included the nature and length of the truce, a system to monitor the border crossings and how reconstruction would be carried out, said Taha.
"We are ready for any help in this issue (of reconstruction), but we are not willing to make it a political issue or use it for blackmail," he told MENA.
First estimates show Gaza suffered about $US2 billion ($A3.05 billion) in damages during the Israeli air strikes and ensuing ground offensive. Israel and the US have opposed reconstruction funds for Gaza going to Hamas.
The issue of new system to monitor the border crossings is key to preserving the ceasefire, and Israel, the United States and Egypt are trying to work out security arrangements to ensure Hamas does not smuggle weapons into the strip before any opening.
Taha told journalists after the talks that the militant group was open to Turkish observers being part of the monitoring system, alongside the Europeans stipulated in a 2005 agreement on the border crossings.
That agreement, supported by Egypt and Israel, also stated that the borders should be controlled by members of Palestinian Prime Minister Mahmoud Abbas' presidential guard.
Hamas forces violently expelled Abbas' soldiers in 2007 leading to the political division of Palestinian lands into Hamas-ruled Gaza and the West Bank controlled by Abbas' Palestinian Authority.
Taha said while the Palestinians monitoring the border could be members of Abbas' security forces, they had to be from the Gaza Strip.
Regarding the issue of the Israeli soldier Sergeant Gilad Schalit, kidnapped by Hamas in 2006, Taha said it would only be discussed as part of a prisoner swap and had no bearing on truce discussions.