Egypt's President Mohammed Morsi said Israel's "aggression" against Gaza will end on Tuesday and Cairo-mediated efforts will produce "positive results" within hours, the official MENA news agency reported.
"The farce of the Israeli aggression will end today, Tuesday, and the efforts to reach a ceasefire between the Palestinians and Israelis will produce positive results within a few hours," it quoted him as saying.
A Hamas official said chief Khaled Meshaal and his negotiators were currently in a meeting with the Egyptian intelligence chief mediating the talks. "But it's no secret we're on the verge of an agreement," he said.
He said Hamas was still insisting Israel lift its six-year blockade the Palestinian enclave for a truce, although it was not clear whether the Jewish state has agreed to this.
Israel on Thursday halted a threatened Gaza ground offensive to give the truce talks a chance, after an overnight meeting of senior Israeli ministers weighed the Egyptian proposal.