At least 49 people have been killed in Gaza since violence escalated on Monday, according to the enclave's health ministry. Six people have been killed in Israel, medical officials said.

In Gaza, a multi-story residential building collapsed after Israel warned its occupants in advance to evacuate, and another was heavily damaged, after they were hit in the air strikes.

Israel said its warplanes had targeted and killed several of the Islamist group Hamas's intelligence leaders. Other strikes hit what the military said were rocket launch sites, Hamas offices and the homes of Hamas leaders.

The heaviest offensive between Israel and Hamas since a 2014 war in the Hamas-ruled enclave has increased international concern that the situation could spiral out of control.

"Israel has gone crazy," said a man on a Gaza street, where people ran out of their homes as explosions rang out.

Many Israelis also spent a sleepless night, with sirens sounding at 3am in Tel Aviv, heralding several waves of rocket strikes in Israel's heartland.

UN Middle East peace envoy Tor Wennesland said the United Nations was working with all sides to restore calm. Egypt made calls overnight to Palestinian leaders to urge restraint.

Israelis ran to shelters or lay flat on pavements in communities more than 70km up the coast from Gaza and into southern Israel as explosions were heard and interceptor missiles streaked into the sky.

An Israeli was killed on Wednesday by an anti-tank missile fired from Gaza at a vehicle near the border, Israel's national ambulance service said. Two people were killed by a rocket that hit their car in Lod, near Tel Aviv.

Lod and other mixed Arab-Jewish towns have been gripped by demonstrations over the Gaza violence and tensions in Jerusalem.

Gaza's health ministry said that of the people reported dead in the enclave, 13 were children.

The Israeli military said it was looking into these reports and that preventing civilian casualties was a priority.

Hamas's armed wing said it fired 210 rockets towards Beersheba and Tel Aviv overnight in response to the strikes on the tower buildings in Gaza City. Israel's military says about a third of the rockets have fallen short, landing within Gaza.

Israeli Defence Minister Benny Gantz said Israeli forces had attacked "many hundreds of targets" and killed senior militants in Gaza and that "all means and options" remained on the table.

"The Israeli military will continue to attack and will bring about complete and long-term quiet," Gantz told reporters. "Only when we achieve this goal, can we talk about calming things down. At the moment, there is no end-date."

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.

These escalated ahead of a court hearing - now postponed - that could lead to the eviction of Palestinian families from East Jerusalem homes claimed by Jewish settlers.

Violence has also flared in the occupied West Bank. Medical sources said a 16-year-old Palestinian was killed in clashes with Israeli forces on Wednesday.

Israeli Prime Minister Benjamin Netanyahu said militants would pay a "very heavy" price for the rocket attacks.

Hamas leader Ismail Haniyeh said Qatar, Egypt and the UN had been in contact, urging calm, but his group's message to Israel was: "If they want to escalate, the resistance is ready, if they want to stop, the resistance is ready."

The White House said on Tuesday Israel had a legitimate right to defend itself from rocket attacks but applied pressure on Israel over the treatment of Palestinians, saying Jerusalem must be a place of coexistence.

Australian Associated Press