"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 senior Hamas official told AFP "the agreement is expected to crystallise in a few hours."
The main sticking point, he said, was whether Israel would begin easing its six-year long blockade of Gaza coinciding with the truce or at a later date.
"A compromise solution is for there to be agreement on lifting the siege, and that it would be implemented later at a specified time," he said.
Israel on Tuesday said it was holding off a threatened Gaza ground offensive to give the truce talks a chance, after an overnight meeting of senior Israeli ministers weighed the Egyptian proposal.
Morsi's announcement comes amid intense diplomatic efforts that brought UN Secretary General Ban Ki-moon on a visit to Cairo on Monday and Israel on Tuesday to bolster efforts to end the week-long conflict.
US Secretary of State Hillary Clinton, on a Southeast Asia tour with President Barack Obama, was also travelling to the region to meet leaders including Israeli Prime Minister Benjamin Netanyahu.
Arab countries meanwhile ratcheted pressure on Israel by sending a delegation of foreign ministers headed by Arab League chief Nabil al-Arabi to Gaza on Tuesday.
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