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 ten 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 this week, and for the first time has struck at Israel's two largest cities, Jerusalem and Tel Aviv. Both cities, more than 70 kilometers (45 miles) from Gaza, had previously been beyond rocket range.
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.