Two Israeli soldiers were killed and seven were wounded in the clashes, the military said.
The violence took a heavy toll on Gaza civilians. Moderate Palestinian leaders called the killings a "genocide" and threatened to call off peace talks.
"The response to these rockets can't be that harsh and heinous," said Palestinian President Mahmoud Abbas. "It is nowadays described as a holocaust."
The spasm of violence came days before Secretary of State Condoleezza Rice was to arrive in the region to nudge Israel and Palestinians closer to a peace accord. But the rising tensions threatened to mar her visit.
Early Sunday, Israeli aircraft destroyed the office building in Gaza City used by Hamas Prime Minister Ismail Haniyeh, witnesses said. Five people were lightly wounded in the raid, seen as a signal that Israel holds the Hamas political leadership responsible for the violence.
While expressing regret for civilian casualties, Israeli Defense Minister Ehud Barak blamed "Hamas and those firing rockets at Israel," his office said in a statement, pledging to continue the offensive to protect Israeli towns and cities.
On Friday, Israeli Deputy Defense Minister Matan Vilnai renewed a threat to invade Gaza to crush militant rocket squads that attack southern Israel daily.
At least two dozen Palestinian civilians, including a baby, were among those killed, and militants said 25 fighters died. Health officials said about 200 people were wounded, 14 of them critically.
The overall death toll was the highest in a single day since the current round of violence erupted in September 2000. The highest previous death toll was 38 on March 8, 2002.
The intense fighting Saturday pushed the Palestinian death toll to more than 80 since fighting flared Wednesday. About half of those were civilians.
Palestinian fighters kept up a steady stream of rocket and mortar attacks on Israeli targets, firing around 50 on Saturday alone in defiance of the Israeli assault. Six Israelis were injured by rockets that reached as far as Ashkelon, a coastal city 11 miles north of Gaza.
The Israeli military said one of its airstrikes on northern Gaza targeted a parked truck loaded with 160 rockets.
On Thursday, militants raised the stakes by firing Iranian-made rockets into Ashkelon, striking closer to Israel's heartland than ever before and putting more Israelis at risk. Palestinian rocket fire earlier in the week also killed an Israeli man.
Shortly before midnight Friday in the northern town of Beit Hanoun, a 13-month-old girl was killed by shrapnel. Hamas blamed Israel, but residents said a militant rocket fell short and landed near the baby's house. The day's violence snowballed from that point on.
Before dawn Saturday, the battleground shifted to the town of Jebaliya and its nearby refugee camp, a center of militant activity in northern Gaza.
Soldiers backed by tanks and aircraft conducted house-to-house searches and took up positions on rooftops as they clashed with militants detonating land mines and firing heavy machine guns, assault rifles and mortar rounds.
A wounded man and boy lay in a gutter near a dead man. Ambulance workers took away the dead man as a youth appealed to paramedics to treat the wounded.
"Take them, they are still alive," he pleaded. Another man urged the wounded to "bear witness," or proclaim their Muslim faith before they die. The two began reciting a Muslim prayer near a boy whose lower body was ripped by shrapnel.
Tareq Dardouna, a Jebaliya resident, said a relative was killed outside his home in the crossfire that began at 3 a.m.
"His body is still on the ground," Dardouna said in a telephone interview from his home, where he was tending to four wounded people amid screaming children. "Ambulances tried to come, but they came under fire. ... We are in a real war."