Palestine’s Hamas fired a barrage of rockets at Israel's economic hub Tel Aviv Tuesday in retaliation for an Israeli strike that destroyed a 12-storey building in Gaza, as the foes traded their heaviest fire for several years.

The sharp escalation, sparked by violence in Jerusalem, has killed at least 28 Palestinians in the blockaded Gaza Strip and three Israelis, prompting international calls for calm.

Several nights of clashes between Palestinian protesters and Israeli police, particularly around the flashpoint Al-Aqsa mosque compound, spiralled on Monday night into a barrage of Islamist rocket fire from Gaza and deadly Israeli air strikes in retaliation.

An Israeli woman was killed as rockets hit Rishon Letzion near Tel Aviv, while in nearby Holon, AFP photographers saw several cars and a bus on fire.

Israel suspended traffic at its main airport on Tuesday due to "massive rocket fire", the aviation authority told AFP, and air traffic websites showed flights redirected to nearby Cyprus.

Hamas, which controls Gaza, said the tower block struck earlier had been a residential building, but AFP reporters said it also houses offices of several Hamas officials.

In the crowded coastal enclave, 10 children were among those killed since Monday night, while 150 people were reported wounded, many rescued from the smouldering ruins of buildings.

Rockets fired by militants in Gaza killed two women a short distance up the coast in Ashkelon, which Hamas threatened to turn into "hell". At one stage the group claimed to have fired more than 100 rockets in under five minutes to overwhelm air defences. At least 84 Israelis have been injured.

Prime Minister Benjamin Netanyahu warned that Israel planned "to further intensify the power of our attacks".

'Fighting will intensify'

Israel's army said more than 600 rockets had been fired since Monday from Gaza towards Israel mainly by Hamas, which rules Gaza, and the Islamic Jihad group.

Many landed inside Gaza or were taken out by Israel's Iron Dome air defence system.

Army spokesman Jonathan Conricus said Israel estimated it had killed 20 Islamist militants in Gaza, warning that "our expectation is the fighting will intensify".

Asked about unconfirmed reports that Hamas was seeking a ceasefire, Conricus said: "I don't think my commanders are aware, or particularly interested."

A Palestinian was also killed and another wounded Tuesday by Israeli army gunfire in the north of the occupied West Bank, a Palestinian security source told AFP.

The Israeli army reported an attempted drive-by shooting, saying "two assailants were neutralised at the scene".

The United States on Tuesday urged both sides to avoid "deeply lamentable" civilian deaths.

"Israel does have a right to defend itself," State Department spokesman Ned Price said, adding: "we don't want to see provocations."

'You escalate, we escalate'

Weeks of tensions boiled over when Israeli riot police clashed with crowds of Palestinians at Jerusalem's Al-Aqsa mosque, on the last Friday of the Muslim holy month of Ramadan.

Nightly clashes since then at the compound, which is holy to both Muslims and Jews, and elsewhere in east Jerusalem have left at least 700 Palestinians injured.

Hamas had warned Israel on Monday to withdraw all its forces from the mosque compound and the Jerusalem district of Sheikh Jarrah, where looming evictions of Palestinian families have fuelled protests.

Sirens wailed across Jerusalem just after the deadline as people in the city, including lawmakers in the Knesset legislature, fled to bunkers for the first time since the 2014 Gaza conflict.

Hamas' Qassam Brigades warned Israel: "if you respond we will respond, and if you escalate we will escalate".

Diplomatic sources told AFP that Egypt and Qatar, who have mediated past Israeli-Hamas conflicts, were attempting to calm tensions.

But Egypt's Foreign Minister Sameh Shoukry told an emergency Arab League meeting that although Cairo had "extensively reached out" to Israel and other countries, "we did not get the necessary response".

'Taking off gloves'

Large protests were held in solidarity with Palestinians around the world, including in London, as well as in Muslim-majority countries including Kuwait, Oman, Pakistan, Tunisia and Turkey.

In Jordan, protesters gathered outside the Israeli embassy, burning Israeli flags and chanting "Shame, shame the embassy is still there" and "Death to Israel".

Jerusalem braced for more protests in which Palestinians hurl rocks, bottles and fireworks at Israeli officers in riot gear, who respond with rubber bullets, stun grenades and tear gas.

"They shot everyone, young and old people," claimed Palestinian man Siraj, 24, about Israeli security forces in a confrontation in which he suffered a spleen injury from a rubber bullet.

Amnesty International accused Israel of using "abusive and wanton force against largely peaceful Palestinian protesters".

Police commissioner Kobi Shabtai told Israeli TV on Monday that in Jerusalem in recent days "we showed too much restraint. We are at the stage of taking off the gloves."