Israel Prime Minister Benjamin Netanyahu.
"Hamas is responsible for the rocket fire and all other attempts to harm our soldiers and civilians, even when other groups participate. And it is Hamas that will pay the heavy price," Defence Minister Ehud Barak said Sunday.
"We will strike with an ever-growing intensity," he added.
Hours later the Israeli airforce carried out several raids on the Gaza Strip overnight. The air raids targeted a smuggling tunnel and an arms cache in the northern Gaza Strip as well as a rocket launch site in the area, a military spokesperson said, adding that the targets had been hit.
The flare-up, which began Saturday, as well as tough statements from Israeli officials, raised the spectre of a broader Israeli operation against Gaza, along the lines of its devastating Operation Cast Lead over the New Year of 2009.
"During the last two days, the IDF [Israel Defence Force], upon my instruction, has been evaluating the host of options for harsher responses against Hamas and the other terror organisations in Gaza," Barak said.
In December 2008, just six weeks before general elections, Israel launched a huge operation in Gaza against rocket fire. The 22-day war killed 1 400 Palestinians – half of them civilians – and 13 Israelis, 10 of them soldiers.
Cairo stepped into its usual role as mediator and was attempting to secure a truce, Egyptian security sources told AFP. Palestinian officials confirmed the initiative and said that the two main militants groups in the Gaza Strip, Hamas and the Islamic Jihad, were ready to respect a truce as of Sunday night "provided Israel commits to doing the same".
The latest violence comes ahead of Israeli elections in January. Prime Minister Benjamin Netanyahu warned earlier that Israel is "prepared to escalate" its response to Palestinian rocket fire.
"The army is acting and will act forcefully against the terror organisations in the Gaza Strip. They are receiving strong blows from the army," Netanyahu told a meeting of his Cabinet.
"The world must realise that Israel won't sit by idly in the face of attempts to attack us. We are prepared to escalate our actions," he said.
The flare-up erupted on Saturday when Gaza militants fired an anti-tank missile at an Israeli jeep along the Gaza border, injuring four soldiers, one of them severely. Three remained in hospital on Sunday.
Israel retaliated with air strikes, shelling and artillery fire that killed six Palestinians and wounded 35 by Sunday night. Palestinian militants fired at least 85 rockets into southern Israel, leaving four injured in the Israeli border town of Sderot.
Two rockets were intercepted by Israel's missile defence system Iron Dome. "It's a very severe situation, rockets are landing on our towns and villages, almost on a daily basis and of course no democratic country can tolerate such a thing," said Finance Minister Yuval Steinitz, a Netanyahu confidant.
US ambassador Dan Shapiro, writing on Facebook, said American "thoughts are with the residents of southern Israel, who continue to be bombarded with missile attacks from terrorist organisations in Gaza".
"The United States supports Israel's right to defend itself and its citizens from these attacks," he said.
Meanwhile newly re-elected US President Barack Obama told Palestinian President Mahmud Abbas on Sunday that his administration opposes a Palestinian bid for non-state membership of the UN, the Palestinian leader's spokesperson said.
"There was a long telephone conversation between president Mahmud Abbas and Barack Obama," Nabil Abu Rudeina told AFP.
"Obama expressed the opposition of the United States to the decision to go to the UN General Assembly."
Groups vow reviews
The Israeli military said it had attacked seven targets on Saturday night, including arms dumps, a weapons-making facility and two rocket-launching sites "in response to recent events".
Medics said 35 people were wounded, with Ashraf al-Qudra, spokesperson for the Hamas-run health ministry, adding that 10 had undergone amputations.
He named the four civilians killed as 20-year-old Matar Abul Ata, 17-year-old Mohammed Harara, 15-year-old Ahmed Harara and 18-year-old Ahmed Dardasawy. There were no immediate reports of any casualties for Sunday night's air raids.
The upsurge in violence has prompted authorities on both sides of the border to close some schools, and in Gaza the Hamas government and militant groups vowed revenge.
"The occupation attacked Palestinian civilians east of Gaza City and Khan Yunis. We consider this escalation as very dangerous. It must stop immediately," said Hamas spokesperson Fawzi Barhum.
The radical Popular Resistance Committees vowed "the Zionist enemy will pay a high price for this crime against Gaza".
And Islamic Jihad warned that "every aggression against the Palestinian people will be followed by a response".
Tensions have been rising on the border since Thursday, when an Israeli soldier was wounded after explosives packed into a border tunnel were detonated in an attack claimed by Hamas's armed wing.
Hours earlier, a 13-year-old Palestinian was shot dead by gunfire from an Israeli helicopter in the same area. – Sapa-AFP