The fighting - which has killed six Palestinians, five of them militants, and a Palestinian man in Israel since Monday -threatened to derail efforts by the United Nations, Egypt and Qatar to broker a long-term ceasefire and head off another major conflict in the impoverished, densely populated enclave.
Hamas, Gaza's dominant Islamist movement, and other armed factions fired over 400 rockets or mortar bombs across the fenced border after carrying out a surprise guided-missile attack on Monday on a bus that wounded an Israeli soldier, the military said.
The salvoes were the fiercest since the seven-week Gaza war in 2014 between Israel and Gaza militants. Hamas said it was retaliating for a botched Israeli commando raid in Gaza that killed one of its commanders and six other gunmen on Sunday. An Israeli colonel was also killed in that incident.
In Gaza City, people gathered in front of a large mound of debris that was once a multi-floor structure. It was flanked by five-storey buildings still standing after the air strike, their shattered stone facades adding to the tall pile of rubble.
In the Israeli coastal city of Ashkelon, a video shot by a resident showed a bleeding woman, lying in the debris of an apartment and covered by dust, weakly raising her arm. She was taken to hospital in critical condition.
The body of a man, killed when a rocket hit the home, was next to her. He was identified by Israeli officials as a Palestinian from Halhoul, in the Israeli-occupied West Bank. Israel Radio said he had a permit to work in Israel.
Israeli Prime Minister Benjamin Netanyahu, who said on Sunday he hoped to avoid another Gaza war and reach an "arrangement" that would also ease Palestinian economic hardship, convened his security cabinet to discuss Israel's next moves.
A Palestinian official said Egypt and the United Nations had stepped up efforts to end the current round of fighting. Since the 2014 war, both Hamas and Israel have pulled back after brief bouts of fighting from another large-scale conflict.
Sirens again rang out in southern Israeli towns on Tuesday after Palestinian rockets crashed into several homes overnight. The military said the Iron Dome anti-rocket system intercepted more than 100 projectiles.
Israel responded with dozens of air strikes, hitting buildings overnight that included a Hamas intelligence compound and the studios of Hamas's Al-Aqsa Television, whose employees had received advance warnings from the military to evacuate.
In aerial attacks on Tuesday, Israel's military said it took out a rocket-launching squad and fired at several Palestinians infiltrating through the border fence around Gaza, which Israel keeps under blockade.
A statement issued by militant groups in Gaza said Ashdod, a major Israeli port just north of Ashkelon, and Beersheba, the biggest city in southern Israel, would be hit next if Israel didn't cease fire.
In Gaza, Israeli missiles flattened seven buildings, mostly in Gaza City including the TV station. Witnesses said warning missiles, which carry small warheads, were fired first.
Abdallah Abu Habboush, 22, said he was awakened by shouts from neighbours to get out of his residential building after what Israel terms the "tap on the roof" warning. They all gathered in a room on the first floor to wait out the attack.
"Old men who were with us fainted because of the smoke," he said, adding that he had no idea why the structure was hit. Conricus said all of the buildings targeted by the Israeli military were "owned, operated and used by Hamas".
Egypt, which borders Gaza to the south, urged Israel to back down. The United States, whose peace mediation has been stalled since the seven-week war in 2014, condemned Hamas.
Violence has simmered since Palestinians launched weekly border protests on March 30 to demand the easing of the blockade on Gaza and rights to lands lost in the 1948 war of Israel's founding. Israeli troops have killed more that 220 Palestinians during the confrontations, which have included border breaches.
Hamas, which is branded a terrorist group in the West, and Israel have fought three wars since the Islamist movement took control in Gaza in 2007, two years after Israel withdrew settlers and soldiers from the small coastal territory. (Writing by Jeffrey Heller and Dan Williams Editing by Andrew Heavens)
(This story has not been edited by Devdiscourse staff and is auto-generated from a syndicated feed.)