Exchanges of fire triggered by Israel's targeted killing of a top militant in Gaza continued for a second day as the Palestinian death toll rose to 26.
Fresh rocket barrages were fired at Israel, which responded with strikes on what it said were Islamic Jihad militant sites and rocket-launching squads in the Gaza Strip.
Israel said it targeted two Islamic Jihad militants preparing to fire anti-tank missiles.
Air raid sirens sounded and fireballs exploded as air defence missiles intercepted rockets, sending Israelis rushing to bomb shelters.
In Gaza, residents surveyed damage and mourned the dead outside a mortuary and at funerals.
Meanwhile, United Nations envoy Nickolay Mladenov has arrived in the Egyptian capital Cairo, airport officials said, following reports he was to hold talks on halting the fighting.
The UN and Egypt have been instrumental in mediating previous ceasefires between Israel and Gaza-based militants.
But a source close to the discussions aimed at mediating a truce warned that the risk of further escalation remained high.
Israeli Prime Minister Benjamin Netanyahu said Islamic Jihad must stop its stop rocket attacks or "absorb more and more blows".
He reiterated his warning that "this could take time" and said Israel would respond to attacks "without mercy".
Islamic Jihad spokesman Musab al-Barayem said the group was not interested in mediation for now as it retaliated to the killing of one of its commanders.
Israel killed senior Islamic Jihad commander Baha Abu al-Ata and his wife Asma in a targeted strike early yesterday, prompting barrages of tit-for-tat rocket fire and air strikes.
According to Israel, he was responsible for rocket fire at Israel as well as other attacks and was planning more violence, with the military calling him a "ticking bomb."
The flare-up raised fears of a new all-out conflict between Israel and Palestinian militants in Gaza, who have fought three wars since 2008.
A total of 26 Palestinians had been killed, including Ata and his wife as well as three children, according to Gaza's Hamas-run health ministry. More than 70 people were injured.
Islamic Jihad confirmed the dead included other members of its armed wing.
360 rockets fired from Gaza since Ata death
Since Israel's killing of Ata in what is believed to have been a drone strike, at least 360 rockets have been fired into Israel from Gaza and dozens have been intercepted by air defences, according to the army.
There have been no Israeli deaths, though damage has been caused and one rocket narrowly missed cars on a busy highway.
Israeli medics said they had treated 48 people with light wounds, while schools were closed in areas near the Gaza border for a second day running.
Schools in the blockaded Gaza Strip, an enclave of two million people, have been closed since yesterday.
Unusually and in a sign it was seeking to avoid a wider conflict, Israel's announced targets were confined to Islamic Jihad sites and not those belonging to Hamas.
It normally holds Hamas, the Islamist movement that rules the Gaza Strip, responsible for all rocket fire from the enclave as the territory's de facto rulers.
The flare-up comes at a politically sensitive time for Israel.
A 17 September general election ended in a deadlock and a new government is yet to be formed. It was the second election since April, when polls also ended inconclusively.
The violence has drawn international calls for calm.