Hamas says Egyptian efforts to broker a truce with Israel have been held up because the Israeli government had yet to respond to proposals.
It is now unlikely a ceasefire will be declared for another 24 hours at the earliest.
Earlier Hamas said it expected the success of peace talks with Israel would allow a truce to be declared at 1900 GMT on Tuesday, to go into effect three hours later.
Prime Minister Benjamin Netanyahu said earlier he was open to a deal to halt Palestinian rocket attacks.
A government told CNN that a ceasefire deal has not been finalised, saying the ball is still in play.
Earlier, President Mohammed Morsi of Egypt was quoted by the state news agency as saying that he expects Israeli forces to end their air strikes on Gaza later on Tuesday.
The official Mena news agency reported that President Mursi said Israel's "aggression" against Gaza would end on Tuesday and Egypt's mediation efforts would produce "positive results" shortly.
The content of the Egyptian plan is not known, but both Israel and Hamas have presented conditions.
The BBC also reports Israel says it has put plans for a land invasion of Gaza on hold.
But the military has also told villagers in north, south and east of Gaza to move to central areas for their own safety.
Leaflets dropped in a number of villages say:
"The Israel Defense Forces are not targeting any of you and they do not want to harm you or your families. For your safety we demand you to evacuate your houses immediately and move towards the centre of Gaza city."
Correspondents say there was a reduced level of activity by both sides on Tuesday. The Israeli military said about 90 rockets had been fired from Gaza toward Israel, and that more than 50 had been intercepted by the Iron Dome missile defence system.