Rocket alarms sounded in towns near Israel's border with Gaza early on Saturday, after the Israeli military carried out overnight strikes on the Palestinian Islamic Jihad militant group.
The exchange of fire between the Israeli military and the militants continued for a fifth day amid reports that both sides were considering a new ceasefire proposal by Egypt after an earlier plan fell through on Friday.
The Israeli military said on Twitter that several PIJ targets in Gaza were hit during the night, including rocket and mortar launching sites and two command centres operated by senior militants identified as Mohammed Abu Al Ata and Khaled Azzam.
The Twitter posts were accompanied by grainy black and white footage showing explosions and clouds of smoke rising from bombed sites.
National Security Adviser Tzachi Hanegbi said on Saturday that Israel's top priority was maintaining its attacks on the Gaza militants.
"We're not holding ceasefire talks," Mr Hanegbi said at a municipal event near Jerusalem.
Six PIJ commanders have been confirmed killed since Tuesday, when Israeli forces launched a campaign against the group, accusing it of planning attacks.
PIJ, the largest armed faction in Gaza after the ruling Hamas group, has since fired almost 1,000 rockets, some deep into Israel. One woman was killed on Thursday when an apartment was struck by a rocket in a Tel Aviv suburb.
At least 33 Palestinians have been killed in Gaza, including women and children, according to health authorities.
Israel says four Palestinians were killed by misfired Gaza rockets, which the PIJ has denied.
There was cautious optimism that a truce might be reached on Friday, with a PIJ source saying a deal drawn up by Cairo had been circulated among the group's leadership.
But the source subsequently said Israel was “disrupting Egypt's efforts for a ceasefire”.
Late on Friday, a Palestinian source said Egypt had circulated a new ceasefire formula. “The Palestinian side is going to study it,” the source said, adding that Egypt was also waiting for Israel's response.
Israeli public television meanwhile said an “improved” Egyptian ceasefire proposal had been handed to Israel.
Israel’s Channel 12 reported that under the new offer, the PIJ was no longer demanding that Israel permanently end assassinations of its commanders, or hand over the body of Khader Adnan, a member of the group whose death while on hunger strike in Israeli custody precipitated the current round of conflict.
The exchange of fire across the Israel-Gaza border extends more than a year of resurgent Israeli-Palestinian violence that has claimed the lives of more than 140 Palestinians and at least 19 Israelis and foreigners since January.
On Saturday, Israeli forces shot dead two Palestinian men during a raid on the Balata refugee camp near the West Bank city of Nablus, the Palestinian news agency Wafa reported.
Three Palestinians, including an elderly woman, were injured but in stable condition, Wafa said, citing the Palestinian Health Ministry and the Red Crescent.
It said the men killed, identified as Saed Jihad Masheh, 32, and Adnan Wasim Araj, 19, were shot in the head.
Israeli forces have launched repeated raids targeting suspected Palestinian militants in the West Bank since a spate of attacks in Israel early last year.
