In a psychological boost for Israel, a new rocket-defense system known as "Iron Dome" knocked down a rocket headed toward Tel Aviv, eliciting cheers from relieved residents huddled in fear after air raid sirens sounded in the city.
Associated Press video showed a plume of smoke following an intercepting missile out of a rocket-defense battery deployed near the city, followed by a burst of light overhead as it struck its target.
Police said a second rocket also targeted Tel Aviv. It was not clear where it landed or whether it was shot down. No injuries were reported. It was the third straight day the city was targeted.
Israel says the Iron Dome system has shot down some 250 of 500 rockets fired toward the country this week, most in southern Israel near Gaza.
Saturday's interception was the first time Iron Dome has been deployed in Tel Aviv. The battery was a new upgraded version that was only activated on Saturday, two months ahead of schedule, the Defense Ministry said.
Israel has vowed to stage a ground invasion, a scenario that would bring the scale of fighting closer to that of a war four years ago. Hamas was badly bruised during that conflict but has since restocked its arsenal with more and better weapons. Five years after seizing control of Gaza, it has also come under pressure from smaller, more militant groups to prove its commitment to fighting Israel as it turns its focus to governing the seaside strip.
Israel's Defense Minister Ehud Barak has authorized the emergency call-up of up to 75,000 reserve troops ahead of a possible ground offensive. Israel has massed thousands of troops and dozens of tanks and armored vehicles along the border in recent days.
Egypt, which is led by Hamas' parent movement, the Muslim Brotherhood, has been spearheading efforts to forge a cease-fire. Morsi has vowed to stand strong with the people of Gaza and this week recalled Cairo's ambassador from Israel to protest the offensive.
Quietly, though, non-Muslim Brotherhood members in Morsi's government are said to be pushing Hamas to end its rocket fire on Israel. Morsi is under pressure not to go too far and risk straining ties with Israel's ally, the United States.
The Hamas website said Saturday that its leader, Khaled Meshaal, met with the head of Egyptian intelligence for two hours Saturday in Cairo, a day after the Egyptian official was in the Gaza Strip trying to work out an end to the escalation in violence.
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 home to 1 million Israelis, finally ends. Past cease-fires have been short lived.
Israeli Prime Minister Benjamin Netanyahu said he spoke with the leaders of Britain, Poland, Portugal, Bulgaria to press his case. "No government in the world would allow a situation where its population lives under the constant threat of rockets," Netanyahu told them, according to a statement from his office.
The diplomatic activity in Cairo illustrated Hamas' rising influence in a changing Middle East. The Arab Spring has brought Islamists to power and influence across the region, helping Hamas emerge from years of isolation.
Morsi warned that a ground operation by Irael will have "repercussions" across the region. "All must realize the situation is different than before, and the people of the region now are different than before and the leaders are different than before," he said at a joint press conference with Turkey's Islamist prime minister, Recep Tayyip Erdogan. Erdogan, like Morsi, leads an Islamist government that has chilly diplomatic ties with Israel.
On Friday, Morsi sent his prime minister to Gaza on a solidarity mission with Hamas. And on Saturday, Tunisia's Foreign Minister Rafik Abdessalem visited Gaza as well.
Joe Federman reported from Jerusalem. Associated Press writers Karin Laub in Gaza City and Aya Batrawy in Cairo contributed reporting.