The US, the European Union and the UK have urged Israel and the Palestinians to lower tensions as soon as possible.
The violence escalated on Monday night after Palestinian militants fired rockets toward Jerusalem.
In response, the Israeli military launched air strikes against militant targets in the Gaza Strip.
Palestinian health officials in Gaza said 22 people, including children, had died in the strikes. Israel’s military said at least 15 members of the Hamas group that rules Gaza were among those killed.
Hamas had threatened to strike after hundreds of Palestinians were injured in clashes with Israeli police at a holy site in Jerusalem on Monday.
Israel’s Prime Minister Benjamin Netanyahu said Hamas had “crossed a red line” and that Israel would respond “with great force”.
The past few days have seen the worst violence in Jerusalem for years.
Increasingly violent confrontations between Israeli police and Palestinian protesters at a compound in Jerusalem’s Old City have threatened to trigger a wider conflict.
Palestinians have been angered about restrictions on access to the compound, where the al-Aqsa mosque – the third holiest site in Islam – is housed, along with the Temple Mount – the holiest site in Judaism.
Early on Tuesday, the Palestinian Red Crescent, a humanitarian group, said more than 700 Palestinians had been injured in clashes with Israeli security forces in Jerusalem and across the West Bank.
Bombardments did not abate overnight as the sound of Palestinian rockets and Israeli air strikes echoed across the region on Tuesday morning.
Meanwhile, Hamas fired at rocket barrage at the city of Ashkelon in southern Israel. It said this was retaliation for an Israeli attack on a civilian apartment block near Gaza city.
A Hamas source told the BBC more than 300 rockets had been fired from Gaza in the last 12 hours.
What’s the global reaction?
US Secretary of State Antony Blinken said Hamas must end the rocket attacks “immediately”, adding: “All sides need to de-escalate.”
White House spokeswoman Jen Psaki echoed those calls, saying US President Joe Biden was seriously concerned about the violence.
In a tweet, UK Foreign Secretary Dominic Raab said the rocket attacks “must stop”, calling for “an end to targeting of civilian populations”.
The EU’s foreign policy chief, Josep Borrell, said the “significant upsurge in violence” in the West Bank, Gaza and East Jerusalem “needs to stop immediately”.
“The firing of rockets from Gaza against civilian populations in Israel is totally unacceptable and feeds escalatory dynamics,” the spokesman said.
The UN Security Council held an urgent meeting Monday over the violence. No statement has been issued.
But speaking to the Associated Press, a diplomatic official said the UN, Egypt and Qatar, which often mediate between Israel and Hamas, were all trying to halt the fighting.
Why is Jerusalem a flashpoint?
The city, with its sacred sites, is the most sensitive place of all in the decades-old conflict between Israel and the Palestinians.
Alongside its religious importance are national claims – Israel in effect annexed East Jerusalem and considers the entire city its capital, though this is not recognised by most other countries.
Palestinians claim the eastern half as the capital of a hoped-for state of their own.
The hilltop compound containing the al-Aqsa mosque and buttressed by the Jewish holy site of the Western Wall is especially sensitive, with both Israel and Palestinians wary of each other’s intentions and activities there.
Israel says the current violence there was planned “well in advance” by Palestinian extremists, though a series of events has driven unrest in Jerusalem.
On Monday, a planned march by Israeli nationalists which was due to pass through Muslim areas of East Jerusalem’s Old City was called off over fears it could stoke unrest.
The Jerusalem Day event marks Israel’s capture of East Jerusalem in 1967.
It is regarded by many Palestinians as a deliberate provocation. This year’s march would also have taken place in the final days of the Islamic holy month of Ramadan.