Palestinian militants bombarded Israel with dozens of rockets and mortar shells Monday, while Israeli warplanes struck targets throughout the Gaza Strip in what appeared to be the most intense exchange of fire since a 2014 war.

Palestinian officials said at least three people, including two militants, were killed by Israeli fire and nine were wounded, and an Israeli airstrike destroyed the ruling Hamas's Al-Aqsa TV station. In Israel, the national rescue service said at least 20 people were wounded, including a 19-year-old soldier and a 60-year-old woman who were in critical condition.

Israeli medical services said a man was killed by a rocket that hit an apartment building in southern Israel and a woman was critically wounded. Magen David Adom said the two were trapped in an apartment in Ashkelon that was struck by a rocket from Gaza early on Tuesday.

Gaza's health ministry, meanwhile, said a 22-year-old Palestinian who was wounded in an earlier airstrike died, putting the Palestinian death toll since the current flare-up started late Sunday to 11, the majority of them militants.

The botched Israeli raid in Gaza on Sunday left seven Palestinian militants and an Israeli officer dead. The violence has thrown into doubt a series of informal understandings reached in recent days aimed at lowering tensions between Israel and Hamas.

The Israel Defence Forces said there were some 370 rockets launched from Gaza since the current round began on Monday afternoon. About 100 of them were intercepted by Israel's Iron Dome defence system, while Israeli TV showed images of a building on fire in a shopping centre in the southern town of Sderot.

Over 300 rockets were launched from Gaza at Israel this evening. In response, we are striking terror targets throughout the Gaza Strip. <a href="https://t.co/2rfIZv2wT8">pic.twitter.com/2rfIZv2wT8</a> —@IDFSpokesperson

Hamas and the smaller Islamic Jihad group claimed responsibility for the rocket fire in a joint statement.

Islamic Jihad spokesperson Daoud Shehab said the groups decided to retaliate for the deadly Israeli incursion "so the occupation and its supporters know that the lives of our sons come with a price."

Israeli soldiers take cover near the Israel-Gaza border on Monday. (Tsafrir Abayov/Associated Press)

Air raid sirens continued to sound throughout southern Israel, as well as in nearby areas of the West Bank.

Mourners chant 'revenge'

Earlier Monday, thousands of mourners buried the seven militants killed in Sunday's incursion. Hamas leader Ismail Haniyeh led a funeral as masked gunmen in uniforms carried coffins draped in the flag of Hamas's armed wing and mourners chanted "revenge."

Hamas, the militant group that has ruled Gaza since 2007, launched a feverish security sweep across the territory, setting up checkpoints across the territory in a show of force after what appeared to be a major security breach for the militant group. It also restricted movement through crossings with Israel, preventing foreign journalists, local businessmen and some aid workers from leaving the territory.

Hamas also cancelled a weekly beach protest in northwestern Gaza along the border with Israel. The organizers cited "the ongoing security situation."

Hamas said Israeli undercover forces entered the territory in a civilian vehicle late Sunday and exchanged fire with Hamas gunmen. The clashes killed an Israeli lieutenant colonel and prompted Israeli airstrikes and a salvo of rocket fire from Gaza toward Israel.

Egypt, UN urge restraint

"In response to yesterday's crime, the joint command of Palestinian factions announce the beginning of bombardment of the enemy's settlements with scores of rockets," Hamas said in a statement.

Egypt told Israel on Monday it needed to stop an escalation of violence in the Gaza Strip, state TV quoted sources as saying. The sources said Egypt told Israel of the need to commit to the de-escalation process, and also stepped up efforts with the Palestinians in that regard.

<a href="https://twitter.com/hashtag/UN?src=hash&ref_src=twsrc%5Etfw">#UN</a> is working closely with <a href="https://twitter.com/hashtag/Egypt?src=hash&ref_src=twsrc%5Etfw">#Egypt</a> and all concerned to ensure that <a href="https://twitter.com/hashtag/Gaza?src=hash&ref_src=twsrc%5Etfw">#Gaza</a> steps back from the brink. The escalation in the past 24hrs is EXTREMELY dangerous and reckless. Rockets must STOP, restraint must be shown by all! No effort must be spared to reverse the spiral of violence —@nmladenov

The United Nations says it is working with Egypt to broker an end to the fighting.

The office of the UN's Mideast envoy, Nickolay Mladenov, said on Monday that efforts were underway "to ensure that Gaza steps back from the brink."

An Israeli soldier stands near a burning bus after it was hit by a mortar shell fired from Gaza on Monday. (Tsafrir Abayov/Associated Press)

It called for an end to rocket fire, and for restraint "by all."

The cross-border fighting came just days after Israel and Hamas reached indirect understandings, backed by Qatar and Egypt, to allow cash and fuel into Gaza. The understandings are meant to be part of a broader effort to alleviate deteriorating conditions in the impoverished territory after 11 years of an Israeli-Egyptian blockade.

It was not clear if the outbreak of violence would derail those arrangements.

PM returns early

Israeli Prime Minister Benjamin Netanyahu cut short a visit to Paris because of the flare-up and returned to Israel on Monday for consultations with top security officials.

The Hamas military wing, Izzedine al-Qassam, said that in Sunday's incursion, Israeli undercover forces drove about three kilometres into southeastern Gaza, and shot and killed Nour el-Deen Baraka, a mid-level commander in charge of a sensitive area in the southern Gaza Strip town of Khan Younis. Qassam members discovered the car and chased it, prompting Israeli airstrikes that killed several people, the group said.

Mourners carry the body of Hamas militant commander Nour el-Deen Baraka, who was killed during an Israeli raid late Sunday. (Adel Hana/Associated Press)

The military provided few details about the reason for Sunday's raid. The Israeli military chief, Lt.-Gen. Gadi Eisenkot, said a "special force" carried out "a very meaningful operation to Israel's security," without elaborating.

Lt.-Col. Jonathan Conricus, a military spokesperson, said the operation was "not intended to kill or abduct terrorists but to strengthen Israeli security." He said the force faced a "very complex battle" and was able to "exfiltrate in its entirety."

In a tweet after his arrival back home, Netanyahu praised the slain officer, whose identity was being kept confidential for security reasons, and said "our forces acted courageously." The officer's funeral was held Monday.

Months of confrontations

The overnight violence came after several months of confrontations along the Israel-Gaza perimeter fence. Since late March, Hamas has been leading mass marches, with turnout driven by growing despair in Gaza, to try to break the border blockade. The blockade has led to over 50 per cent unemployment and chronic power outages, and prevents the vast majority of Gazans from travelling.

More than 170 demonstrators, most unarmed, have been killed by Israeli army fire in the confrontations, in which some of the participants threw stones, burned tires or hurled grenades toward Israeli forces.

Israel says it is defending its border against militant infiltrations, but its army has come under international criticism because of the large number of unarmed protesters who have been shot.

Last week, Israel allowed Qatar to deliver $15 million US in aid to Gaza's cash-strapped Hamas rulers. Hamas responded by lowering the intensity of the border protest last Friday.

On Sunday, Netanyahu defended his decision to allow through the Qatari cash to Gaza as a way to avert an "unnecessary war," maintain quiet for residents of southern Israel and prevent a humanitarian catastrophe in the impoverished Gaza Strip.