Hamas has offered Israel a one-year truce in Gaza after the latest round of talks in Egypt.
Ayman Taha, a Hamas official, said in Cairo that his delegation was briefed by the Egyptians on an Israeli proposal for an 18-month truce with only a partial opening of the border, which they rejected.
Instead, Mr Taha said 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 said.
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Gaza’s borders are its lifeblood as it is dependent on the outside world for almost all of its services.
The current ceasefire was supposed to last for a week and technically expired at the weekend. But it is expected to last for at least as long as the talks continue.
The flurry of diplomatic activity came as President Barack Obama’s Middle East envoy, George Mitchell, was preparing to leave for the region, where he is due to arrive on Wednesday.