The cross-border violence, which erupted on Monday following weeks of rising tensions in the contested city of Jerusalem, is the worst the region has experienced in years.

More than two dozen Palestinians have been killed in the last day, including several children. Three Israelis died from Gaza rocket fire on Tuesday, DPA news agency reported.

Israeli Prime Minister Benjamin Netanyahu said the attacks on Gaza, which have targeted some 500 Hamas and Islamic Jihad positions since Monday, would intensify.

"This operation will take time, but we will bring security back to the citizens of Israel," he said late Tuesday.

Hamas, which rules the coastal strip, would "receive blows it did not expect," Netanyahu had said hours earlier in remarks after a meeting with military officials.

An Israeli military spokesperson said that at least 20 members from the two groups have been killed so far in Gaza, including senior officials, and some 150 missile-launchers had been destroyed.

Many of the targets were located in places where civilians reside, spokesperson Jonathan Conricus said, so civilian casualties could not be ruled out, though the army was trying hard to avoid them.

Rocket warning sirens were a persistent sound across Israeli communities.

The greater Tel Aviv area was in the cross-hairs of Palestinian militants, who sent a barrage of rockets towards the coastal metropolis, marking the heaviest attack the city has faced so far.

The rocket fire prompted flights to be halted at Israel's main international airport outside of the city.

The Ben Gurion Airport near Tel Aviv was closed to landings and departures due to the attacks; flights were diverted to Cyprus.

One person was killed on the outskirts of Tel Aviv in rocket attack. According to media reports, a woman was killed in the town of Rishon Lezion when she was hit directly. The Zaka aid organization also confirmed her death.

The rockets were fired toward Tel Aviv after the Israeli army destroyed a building containing offices of members of the Hamas political bureau in the Gaza Strip.

Residents of the building were warned by Israeli forces before the attack and told to leave, witnesses said.

A Hamas spokesman had earlier threatened a "harsh" rocket attack on Tel Aviv if the Hanadi Tower building was destroyed.

In the southern city of Ashkelon, two women were killed when their homes were struck, according to the Zaka aid organization. Impacts were also reported on residential buildings in Ashkelon as well as a school where no lessons were being conducted.

In total, Gaza militants aimed around 480 rockets towards Israel over 24 hours. Of these, some 200 were intercepted and 150 failed to properly launch, the Israeli military said Tuesday evening.

The Al-Qassam Brigades, the military wing of Hamas, claimed responsibility for the attacks, which it said were in retaliation for a deadly Israeli strike on a high-rise residential building in the western part of the Gaza Strip. The apartment belonged to a member of Islamic Jihad, according to witnesses.

In total, the Gaza Health Ministry put the death toll in the latest round of violence at 28, including 10 children. More than 100 people were injured, it said.

According to local media and witness reports, three children were killed by Israeli airstrikes and others by misdirected rockets fired by extremists.

Israel said it was targeting rocket production, storage and training facilities as well as military posts.

The airstrikes and rocket attacks followed violent clashes in recent days at Jerusalem's holy site known as the Temple Mount to Jews and the Noble Sanctuary to Muslims.

Demonstrations continued on the ground in Israel on Tuesday between police and Israeli Arabs in numerous cities throughout Israel. Stones were thrown at police officers and several cars were set on fire.

In the city of Lod, a 25-year-old Arab man was shot and killed during the riots. Media reported that a 34-year-old arrested after the event was a Jewish resident of the city.

The Islamist Hamas movement had issued a Monday night ultimatum telling Israel to withdraw settlers and police from the Jerusalem holy site, parts of which had been cordoned off, and from the Sheikh Jarrah neighbourhood.

Shortly after the deadline expired, mass rocket attacks began, with sirens wailing in Jerusalem.

Netanyahu said the militants crossed a "red line" by directing missiles towards Jerusalem, and Israel in turn shelled targets in Gaza.

Leaders around the world expressed concern about the escalating violence, calling on both sides to show restraint.

"This spiralling escalation must cease immediately," a spokesperson for UN Secretary General Antonio Guterres said.