Smoke rises following an Israeli strike on Gaza, as seen from the Israel-Gaza Border, Tuesday, July 8. Photo: AP

Palestinian militants have fired more rockets at Israeli cities after the start of a major air and sea offensive by Israel in the Gaza Strip.

Hamas launched several missiles toward Jerusalem on Tuesday night but did not hit the city. Earlier, Israel also intercepted a rocket fired at Tel Aviv.

The attacks come after a day of multiple Israeli air strikes in Gaza, which killed more than 20 Palestinians.

Israel has accused Hamas of firing hundreds of rockets in recent days.

"No other country lives under such a threat, and no country would accept such a threat," Prime Minister Benjamin Netanyahu said in a statement late on Tuesday.

"We have therefore significantly expanded our operations against Hamas and the other terrorist organisations in Gaza."

Israel has warned it may send ground troops into Gaza to stop the rocket attacks. It has authorised the call-up of up to 40,000 military reservists. Hundreds of reservists have already been drafted to bolster forces around Gaza.

Palestinian Authority President Mahmoud Abbas demanded that Israel immediately stop the raids on Gaza and appealed for calm.

'WAR CRIME'

In addition to launching missiles at Jerusalem and Tel Aviv, Hamas claimed it had also fired rockets at the city of Ashdod and as far as Haifa - some 165km (103 miles) away from Gaza.

There were no reports of anything landing in Haifa, but Israel said a rocket hit Hadera, about 100km away from Gaza.

The military wing of the militant group has warned that all Israelis are now targets.

The Israeli Defence Force said in a tweet that 117 rockets had struck Israel since Monday night, while an additional 29 were intercepted by the Iron Dome missile defence system.

The military confirmed earlier that in response it had targeted some 50 "terror sites" in Gaza on Tuesday.

Israeli officials said aircraft and naval vessels had targeted militant compounds, rocket launchers and other infrastructure in Gaza, which is dominated by Hamas and until recently was governed by it.

Spokesman Lt Col Peter Lerner said Israel was preparing for an "escalation" of the campaign, dubbed "Operation Protective Edge", and would continue its bombardment as long as Israeli citizens were under fire.

Missiles struck the homes of several Hamas operatives who Israel claimed were involved in firing rockets, and what it said was a command centre located in a civilian building.

Among those killed in the raids were four Hamas members who died in Gaza City when their car was struck. One of the dead was Mohammed Shaaban, a senior militant.

Palestinian eyewitnesses also said that Hafez Hamad, a local leader of the Islamic Jihad militant group, was killed in an air strike in northern Gaza.

Later, the home of a Hamas leader in the southern city of Khan Younis was hit, killing six people. Health ministry spokesman Ashraf al-Qudra said two teenage boys were among those killed.

A Hamas spokesman condemned the air strike, calling it a "horrendous war crime".

Separately, the Israeli military released video footage that apparently showed Hamas militants emerging from the sea in diving gear on an Israeli beach before being killed by Israeli troops.

SUDDEN ESCALATION

The government has declared a state of emergency in southern Israel.

In cities and towns within 40km of Gaza, summer camps and schools have been instructed to close and residents have been encouraged to stay near their homes.

The sudden escalation comes just days after suggestions of a truce from both Israel and militant groups in Gaza.

Tensions spiked last week with the murders of three young Israelis in the occupied West Bank and a Palestinian teenager in Jerusalem.

Israel says Hamas was behind the abduction and murder of the Israeli youths - a claim it denies.

A day after their funerals, the Palestinian was abducted in East Jerusalem and murdered. Police have arrested six Jewish suspects and say it seems the 16-year-old was killed because of his nationality.