Palestinians sent a Grad rocket slamming into the Israeli city of Beersheva Wednesday, injuring a man, after Israeli air strikes and a mortar attack killed eight Gazans.

The Al Quds Brigades, Islamic Jihad's armed wing, claimed responsibility for the attack as well as for the overnight firing of another Grad rocket towards the port city of Ashdod, saying it was in response to a series of Israeli attacks a day earlier which killed eight, two of them minors.

Shrapnel from the rocket, which struck the centre of Beersheva, hit a man in the chest, injuring him moderately, officials said.

Shortly afterwards, militants lobbed seven mortar shells into southern Israel, causing no injuries or damage, the army said.

With tensions soaring on the border with Israel after days of rocket fire and riposte air strikes, Israeli aircraft hit a target on the edge of Gaza City early on Wednesday, injuring two Al Quds Brigades militants, one critically, Palestinian medical and security sources said.

Wednesday's rocket attack came a day after Israel mounted a series of raids on targets in the eastern sector of Gaza City, killing eight people.

All eight, two of whom were minors, were to be buried following a collective funeral in central Gaza City at midday, with officials from Gaza's Hamas leadership declaring a day of mourning.

Four of the dead were militants from the Al Quds Brigades whom the army said were trying to fire rockets towards Israel from the Zeitun neighbourhood.

Several hours earlier, four civilians had been killed in the nearby district of Shejaiya when Israeli artillery fired towards a house outside which a group of youngsters had been playing football, Palestinian medics said.

Among the dead were two boys, one who was 11 and another who was 16. Another 12 people were wounded, including three young children.

Overnight, the Al Quds Brigades militants fired a Grad rocket at the southern port city of Ashdod but it fell short, and did not cause injuries or damage. An Israeli airstrike followed soon after, injuring two Al Quds militants, one who was in critical condition.

The surge in bloodshed and cross-border violence has ramped up tensions between Israel and Gaza's Islamist Hamas rulers and again raised fears of a large-scale Israeli military incursion.

After the Beersheva attack, Israeli vice-premier Silvan Shalom, himself from the same neighbourhood where the Grad landed, said Israel should focus its retaliatory strikes on militant leaders.

"Nobody from the leadership has personal immunity," he told Israeli public radio.

"We shouldn't be firing just at open fields or tunnels but acting in such a way that on the other side they understand that they price they will have to pay will be of the heaviest."

The upsurge in bloodshed drew a chorus of both condemnation and concern, both at home and abroad.

Hamas premier Ismail Haniya called on the UN Security Council, "which has not hesitated to take decisions and implement them rapidly, as with Libya, to do the same to protect our people and punish the Israeli occupation," a statement said.

Palestinian president Mahmud Abbas, currently in Moscow, condemned "the Israeli escalation which has cost the lives of many Palestinians, including children," his spokesman Nabil Abu Rudeina said.

And Israeli Prime Minister Benjamin Netanyahu expressed regret over the civilian deaths, but emphasised that the shelling of the house in Shejaiya came in response to Hamas "using civilians as human shields."

"It is unfortunate that Hamas continues to rain dozens of rockets down on Israeli civilians, intentionally using civilians as human shields," he said, insisting that Israel did not want to cause the situation to deteriorate.

UN Secretary General Ban Ki-moon also spoke out, saying he was "very concerned" at the escalating situation in Gaza and southern Israel, a statement from his office said.

"He reiterates as well his condemnation of rocket fire by Palestinian militant groups in Gaza, including from populated areas, against civilian targets in southern Israel," it said, calling on all parties to respect their obligations under international humanitarian law.

In response to the civilian deaths in Shejaiya, the army said it had opened an investigation, while insisting there were "terrorists among the dead."