Israel has launched a fresh air strike on Gaza east of Rafah in which two people have been reportedly killed and another civilian injured, raising the Palestinian death toll to 11.
Sunday's raid came hours after the Islamic Jihad movement in Gaza said it had accepted a ceasefire agreement.
"The Islamic Jihad has responded [positively] to the truce effort, while it reserves its right to react to any aggression [by Israel]," Abu Ahmad, the spokesman for the movement's armed wing, Al-Quds Brigades, said in a statement on Sunday.
The spike in violence came as funerals were being held for two Palestinians killed in Israeli air strikes overnight. Egypt had been mediating truce efforts over the weekend and late on Sunday morning.
Meanwhile, Binyamin Netanyahu, the Israeli prime minister, has blamed Hamas, which governs Gaza, for the violence.
"The Hamas rules Gaza, he is responsible for Gaza, he is responsible for preventing the firing from Gaza, and for keeping the calm in Gaza, even if the attackers are the Islamic Jihad," he said.
An Israeli military official said on Sunday that three rockets were fired at its territory after the ceasefire deadline had passed.
Two of the rockets were intercepted by Israel's Iron Dome missile defence system and another slammed into southern Israel causing no casualties or damage, the official said.
The Israeli military said more than a dozen mortars and rockets had been fired from Gaza since midnight.
Doubt over truce
Al Jazeera’s Cal Perry, reporting from Al Shojaya in eastern Gaza, said that after the latest barrage of fire between Gaza and Israelis, there was an attempt at a ceasefire.
"We heard an Islamic Jihad spokesperson saying that they were going to give 48 hours both to the Egyptians and the Israelis to work out some kind of an agreement.
"But as late as Sunday afternoon, there has been a further air strike bringing into question if anyone is going to be able to stop the recent spate of violence."
Gaza residents reported hearing explosions as Al Jazeera's sources said Israel had embarked on a new round of attacks on Islamic Jihad targets.
Sunday's violence continued after the air strikes a day earlier that killed nine Palestinian fighters in Gaza, and Palestinian rocket fire that killed one person in Israel.
A leader of a Palestinian group, who asked to remain anonymous, told the AFP news agency: "The efforts and intensive contacts led by senior Egyptian intelligence service officials led to a national consensus to restore calm [with Israel]."
But the AP news agency reported earlier that mediation efforts had failed, citing an anonymous Egyptian official.
Gaza fighters 'killed'
Adham Abu Selmiya, a spokesman for Gaza's emergency services, said on Saturday that five members of the Al-Quds Brigades were killed and three wounded in a first Israeli attack on a training camp near Rafah.
The dead included a commander named as Ahmed al-Sheikh Khalil, the group said.
Israeli aircraft later struck more targets in Gaza, witnesses and Palestinian officials said, killing four more Palestinian fighters and wounding two more people.
At least two of those were killed as they tried to fire a Grad rocket into Israel, an Al-Quds spokesman said.
An Israeli strike east of Gaza City and two in the area of Khan Yunis, in the south, caused no casualties, witnesses said.
As rockets and mortar shells were fired into Israel, police raised the level of national alert to its second-highest status.
The Israeli military said the Rafah raid had "targeted a terrorist squad in the southern Gaza strip responsible for the firing of military-use projectiles towards the Israeli home front".
Within hours of the attack, at least 20 Palestinian rockets and mortar bombs hit different sites in southern Israel, wounding three civilians, Israeli police said.
One rocket slammed into a community centre and another into a block of flats, setting parked cars and gas canisters alight.
Rockets hit the city of Ashdod, the nearby town of Gan Yavneh and the city of Ashkelon, to the south, police said.
The Al-Quds Brigades claimed responsibility for the rocket fire and posted a video on its website which it said showed the launching of five of the rockets.
The Popular Front for the Liberation of Palestine also claimed responsibility for the attacks.
And a spokesman for Hamas' Ezzedine al-Qassam Brigades blamed Israel for the escalation.
"The occupation is completely responsible for the crime in Rafah and all of the resistance factions cannot leave the shedding of our martyrs' blood unanswered," Abu Obeida, Hamas spokesman, said. "We shall discuss the answer to this crime."
The air raid and earlier rocket attack were the first violent incidents since October 18 when Hamas repatriated Gilad Shalit, an Israeli soldier it seized in 2006, in exchange for the release of more than 1,000 jailed Palestinians .