Israel has deployed its 'Iron Dome' missile defence system [REUTERS]

Five Palestinians have been killed and around 45 wounded in Israeli air strikes on the Gaza Strip following an offer of a ceasefire from Hamas after a surge in cross-border violence.

An attack on the southern city of Khan Younis killed two members of the al-Qassam Brigades, the armed wing of the Hamas movement, which has fired missiles into Israel in response to Israel's killing of three of its members last week.

Another airstrike near Khan Younis killed three people - an elderly man, a woman and her daughter - and injured others, according to Al Jazeera's correspondent in Gaza, Nicole Johnston.

The Israeli army said in a statement that "uninvolved civilians have apparently been injured" in one strike.

"The IDF regrets that the Hamas terrorist organisation chooses to operate from within its civilian population, using it as a 'human shield'," the statement said.

Two days of fighting have seen ten people killed in Gaza, following a Palestinian rocket attack on an Israeli school bus on Thursday.

Dozens more have been injured, medical sources said.

Around 15 rockets were fired into Israel on Friday, police said, but no casualties were reported.

Both sides have said they hoped to avoid further violence, but an Israeli cabinet minister said the strikes would continue.

"We are acting as we see fit so that this type of fire will not continue, and so that the people behind the fire will regret it,'' Matan Vilnai, in charge of the home front, told Army Radio.

Johnston, Al Jazeera's correspondent, said Hamas "really doesn't want to risk an escalation of violence with Israel, and that is very clear simply by the fact they said they would stick to the ceasefire".

She said only one faction in Gaza had said it would not stick to the ceasefire. "It's one thing for factions and groups to say that they will abide by the ceasefire, but it's another thing to see them actually stick to it," she said.

In Thursday's bus attack, Gaza fighters hit an Israeli school bus near the border with an anti-tank rocket, badly wounding the driver and a 16-year-old boy. The boy remains unconscious in the intensive care ward of an Israeli hospital.

The al-Qassam Brigades said it had shot two missiles early in the day, one of which had hit the school bus. The Brigades said the attack came in reponse to Israel's killing of three of its members last week.

A senior Hamas official told Al Jazeera: "The Israelis are trying to impose a new formula in Gaza. They are trying to prevent us from taking any benefits in the region.

"They are trying to escalate the situation ... The coming few days will carry a lot of developments if things continue like this."

Mahmoud Abbas, president of the Palestinian Authority, has urged western powers to intervene and called on Palestinians "not to give Israel an excuse to hit Gaza".

Israel has been using its latest cutting-edge missile-defense system for the first time since Thursday.

The Iron Dome system scored a direct hit on an incoming Palestinian rocket aimed at an Israeli city, shooting it down, Israel said.

Source: Al Jazeera and agencies