Egypt has been trying to broker a truce in the conflict. The statement came after Israel put plans for a ground operation on hold to give ceasefire talks in Cairo a chance.
The conflict began last Wednesday when Israel killed a Hamas military leader, saying it wanted to end rocket attacks.
More than 110 Palestinians and three Israelis have been killed.
Tuesday has seen a reduced level of violence, correspondents say, even though Israel has conducted some strikes - one was a "direct hit" on two militants in northern Gaza, the Israeli military said.
And rockets have been fired towards Israel - mainly targeting the south. However, two landed in an open area near Jerusalem, causing no injuries or damage.
President Mursi said Israel's "aggression" against Gaza would end on Tuesday and Egypt's mediation efforts would produce "positive results" shortly, the official Mena news agency reported.
Source: BBC News