Israeli warplanes hit a number of targets in the Gaza Strip Thursday night in response to heavy Palestinian rocket fire into the Jewish state earlier, Palestinian eyewitnesses said.

Aircraft hit bases of the strip's Hamas rulers and the armed wing of Islamic Jihad, the Al-Quds Brigades, which had claimed responsiblity for firing dozens of rockets into Israel.

The militant strikes were the biggest wave of attacks since a major eight-day November 2012 confrontation between Israel and militants from Gaza's ruling Islamist movement Hamas.

The witnesses, including an AFP photographer, said there were nine Israeli strikes throughout the coastal strip on facilities operated by Al-Quds and Hamas's military wing, the Ezzedine Al-Qassam Brigades.

There were no immediate reports of casualties.

Hamas personnel, including fighters, had earlier evacuated all their bases, Gaza security sources said.

An Israeli military spokeswoman told AFP warplanes has been in action over the Hamas-ruled territory but did not elaborate.

The earlier Al-Quds barrage, which Israel said came from several sites and police said hit all along southern Israel's border with Gaza, caused no casualties but prompted Prime Minister Benjamin Netanyahu to warn of a tough response.

This escalation in violence between them came just hours after British Prime Minister David Cameron arrived on his first official visit to the region since taking office in 2010.

Al Quds said it had fired 90 rockets at Israel in response to an air strike on Tuesday that killed three of its militants in southern Gaza.

As tens of thousands of people living in southern Israel rushed to seek shelter from the bombardment an Israeli security source told AFP militants had fired more than 60 rockets and mortar rounds.

The army put the number at "more than 30 rockets," saying eight of them had struck urban areas, and another three were intercepted by the Iron Dome anti-missile system.

Police raised the level of alert in the south, saying the rockets struck along the length of Israel's border with Gaza.

One hit near a public library in the town of Sderot, and another near a petrol station.

The attack began shortly after Netanyahu and Cameron addressed parliament, and prompted a stern warning from the Israeli leader, who pledged to act "with great force" against those seeking to harm Israel, a statement from his office said.

"We will continue to strike those who want to harm us; we'll act against them very forcefully," he was quoted as saying in a separate statement communicated by his spokesman Ofir Gendelman.

Later, Netanyahu warned again.

"If there won't be quiet in the south (of Israel) there will be noise in Gaza, and this is an understatement," he said, in remarks relayed by his office.

Defence Minister Moshe Yaalon ordered the closure from Thursday of the Kerem Shalom goods crossing between Israel and Gaza and the Erez pedestrian crossing "until further security assessments," a military statement said.

"This is the biggest attack on Israel since the 2012 Operation Pillar of Defence," the military said on Twitter, referring to the 2012 confrontation that claimed the lives of 177 Palestinians, mostly civilians, and six Israelis.

Foreign Minister Avigdor Lieberman said Israel would have no choice but to reoccupy Gaza, from which it withdrew all troops and settlers in summer 2005.

"Following an attack like this -- a barrage of more than 50 rockets -- there is no alternative to a full reoccupation of the entire Gaza Strip," he told private Channel 2 television.

In Gaza, Islamic Jihad's armed wing the Al-Quds Brigades issued a statement claiming to have fired "70 rockets" at Israel.

It said its bombardment would continue in response to Israel's "aggression" in Tuesday's air strike.

Hamas warned Israel against escalating the confrontation.

"We hold the occupation responsible, we warn of the consequences of any escalation and we reiterate that resistance is the right of the Palestinian people to defend itself," said Ihab al-Ghassin, a spokesman for the Islamist movement Hamas, which governs Gaza.