"There are discussions about the ways to bring a cease-fire soon, but there are no guarantees until now," Morsi said at a news conference. He said he was working with Turkey, Arab countries, the United States, Russia, and western European countries.
Israel launched the operation on Wednesday in what it said was an effort to end months of rocket fire out of the Hamas-ruled territory. An air strike killed Hamas' powerful military chief, and since then Israel has relentlessly targeted suspected rocket launchers and storage sites.
In all, 48 Palestinians, including 15 civilians, have been killed and more than 400 civilians wounded, according to medical officials.
Three Israeli civilians have been killed and more than 50 wounded.
Israeli military officials expressed satisfaction with their progress Saturday, claiming they have inflicted heavy damage to Hamas.
"Most of their capabilities have been destroyed," Maj. Gen. Tal Russo, Israel's southern commander, told reporters. Asked whether Israel is ready to send ground troops into Gaza, he said: "Absolutely."
"Most of their weapons are stored in civilian's homes, they launch rockets from residential areas. We do not want to hit civilians in Gaza but we do want to hit the hornets' nest of terror in Gaza," he said.
Footage released Saturday by the Islamic Jihad showed rockets being fired from a hidden bunker in a built-up area. It wasn't clear whether it was a residential neighborhood.
Israel's Deputy Foreign Minister Danny Ayalon told channel 1 TV that "Hamas is committing a double war crime. They are firing rockets at Israeli civilians while using Palestinian civilians as human shields."
The White House said President Obama was also in touch with the Egyptian and Turkish leaders. The United States has solidly backed Israel.
Speaking on Air Force One, deputy national security adviser Ben Rhodes said the White House believes Israel "has the right to defend itself" against attack and that the Israelis will make their own decisions about their "military tactics and operations."
Despite the bruising offensive, Israel has failed to slow the barrages of rockets from Gaza.
The Israeli military said 160 rockets were launched into Israel on Saturday, raising the total number to roughly 500 since the week's fighting began. Eight Israelis, including five civilians, were slightly wounded Saturday, the army said.
Israel carried out at least 300 air strikes on Saturday, the military said, and it broadened its array of targets. One air raid flattened the three-story office building used by Hamas' prime minister, Ismail Haniyeh. He was not inside at the time.
In southern Gaza, aircraft went after the tunnels that militants use to smuggle in weapons and other contraband from Egypt. Tunnel operators said the intensity of the bombing was unprecedented, and that massive explosions could be heard miles away, both in Gaza and in Egypt.
The operators, speaking on condition of anonymity because of the illicit nature of their business, said they cannot approach the tunnel area to assess the damage, but the blasts appeared to be more powerful than in Israel's last major push to destroy the tunnels during a previous offensive four years ago. The tunnels are a key lifeline for Hamas, bringing in both weapons and supporting a lucrative trade that helps fund the group's activities.
Missiles also smashed into two small security facilities and the massive Hamas police headquarters in Gaza City, setting off a huge blaze that engulfed nearby houses and civilian cars parked outside, the Interior Ministry reported. No one was inside the buildings.
Early on Sunday, Gaza health official Ashraf al-Kidra said two teenagers were killed and 10 people were injured when a building was hit. Gaza residents reported heavy Israeli raids overnight.
Air attacks knocked out five electricity transformers, cutting off power to more than 400,000 people in southern Gaza, according to the Gaza electricity distribution company. People switched on backup generators for limited electrical supplies.
Hamas has unveiled an arsenal of more powerful, longer-range rockets during the fight, and for the first time has struck at Israel's two largest cities, Jerusalem and Tel Aviv. Both cities, more than 45 miles from Gaza, had previously been beyond rocket range.
Hamas has not immediately accepted Egypt's proposal for a cease-fire, but the group's website said it could end its rocket fire if Israel agrees to end "all acts of aggression and assassination" and lift its five-year blockade on Gaza. Egypt will present the Hamas position to Israeli officials.
Israeli officials say they are not interested in a "timeout," and want firm guarantees that the rocket fire, which has paralyzed life in an area that is home to one million Israelis, finally ends. Past cease-fires have been short lived.