The Israeli Defence Forces (IDF) said that they had killed two senior Hamas chiefs, Hassan Kaogi, head of the Hamas military intelligence security department, and his deputy, Wail Issa.
IDF said the intel chiefs were killed by Israeli fighter jets, tweeting “Looks like our intel was better.’.
The Palestinian death toll was 36 on Wednesday morning, with ten children among the dead.
Five Israelis are believed to have been killed in the conflict, in the most intensive aerial exchanges for years.
Israel carried out hundreds of air strikes in Gaza into Wednesday morning, as the Islamist group and other Palestinian militants fired multiple rocket barrages at Tel Aviv and Beersheba.
One multi-storey residential building in Gaza collapsed and another was heavily damaged after they were repeatedly hit by Israeli air strikes.
Other strikes targeted what the military said were rocket launch sites, Hamas offices and the homes of Hamas leaders.
It was the heaviest offensive between Israel and Hamas since a 2014 war in Gaza, and prompted international concern that the situation could spiral out of control.
U.N. Middle East peace envoy Tor Wennesland tweeted: “Stop the fire immediately. We’re escalating towards a full scale war. Leaders on all sides have to take the responsibility of de-escalation.
“The cost of war in Gaza is devastating & is being paid by ordinary people. UN is working w/ all sides to restore calm. Stop the violence now,” he wrote.
Gazans homes shook and the sky lit up from Israeli attacks, outgoing rockets and Israeli air defence missiles intercepting them. At least 30 explosions were heard within a matter of minutes just after dawn on Wednesday.
Israelis ran for shelters or flattened themselves on pavements in communities more than 70 km (45 miles) up the coast and into southern Israel amid sounds of explosions as interceptor missiles streaked into the sky.
In the mixed Arab-Jewish town of Lod, near Tel Aviv, two people were killed after a rocket hit a vehicle in the area.
Lod and other mixed towns have been gripped by angry demonstrations over the Gaza violence and tensions in Jerusalem.
Hamas’s armed wing said it fired 210 rockets towards Beersheba and Tel Aviv in response to the bombing of the tower buildings in Gaza City.
Israel’s military says that around a third of the rockets have fallen short, landing within Gaza. It actually estimated the rockets at 1,050, fired in 38 hours across central and southern Israel.
For Israel, the militants’ targeting of Tel Aviv, its commercial capital, posed a new challenge in the confrontation with the Islamist Hamas group, regarded as a terrorist organisation by Israel and the United States.
The violence followed weeks of tension in Jerusalem during the Muslim fasting month of Ramadan, with clashes between Israeli police and Palestinian protesters in and around Al-Aqsa Mosque, on the compound revered by Jews as Temple Mount and by Muslims as the Noble Sanctuary.
These escalated in recent days ahead of a – now postponed – court hearing in a case that could end with Palestinian families evicted from East Jerusalem homes claimed by Jewish settlers.
Violence has also flared in the occupied West Bank, where a 26-year-old Palestinian was killed by Israeli gunfire during stone-throwing clashes in a refugee camp near the city of Hebron.
‘A VERY HEAVY PRICE’
There appeared no imminent end to the violence. Israeli Prime Minister Benjamin Netanyahu warned that militants would pay a “very heavy” price for the rockets, which reached the outskirts of Jerusalem on Monday during a holiday in Israel commemorating its capture of East Jerusalem in a 1967 war.
The outbreak of hostilities led Netanyahu’s political opponents to suspend negotiations on forming a coalition of right-wing, leftist and centre-left parties to unseat him after an inconclusive March 23 election.
Opposition leader Yair Lapid has three weeks left to establish a government, with a new election – and another chance for Netanyahu to retain power – likely if he fails.