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.
Air raid sirens wailed 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.
UN envoy Nickolay Mladenov was expected in Cairo for talks on halting the fighting, a diplomatic source said, but a source close to the discussions warned the risk of further escalation remained high.
In comments Wednesday morning, 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 responded 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 Tuesday, prompting barrages of retaliatory Palestinian rocket fire followed by Israeli air strikes.
According to Israel, Ata 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 conflict between Israel and Palestinian militants in Gaza, who have fought three wars since 2008.
A total of 22 Palestinians have been killed so far, including Ata and his wife, according to Gaza’s Hamas-run health ministry.
Islamic Jihad confirmed that the dead included other members of its armed wing.
More than 200 rockets, schools still closed
Since Israel’s killing of Ata in what was believed to be a drone strike, at least 220 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.
On Tuesday, school closures included the commercial capital Tel Aviv.
Schools in the blockaded Gaza Strip, an enclave of two million people, have been closed since Tuesday.
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.
Israel 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. Islamic Jihad is the second most-powerful militant group in the Gaza Strip.
Israeli analysts were quick to highlight the change of approach.
“For the first time in the current era, Israel drew a distinction between Hamas and Islamic Jihad,” commentator Ben Caspit wrote in Israeli newspaper Maariv.
“By so doing, Israel deviated from its iron-clad principle that Hamas, as the sovereign power in Gaza, has to pay the price for any action taken by anyone in the Gaza Strip. That is now no longer the case.”
For their part, Hamas rulers have yet to enter the fray. With Gaza’s economy in tatters, they appear to have little desire for another round of fighting with Israel.
The violence drew international calls for calm.
Britain’s foreign office said “we call on all sides to rapidly de-escalate the situation, and support the UN and Egyptian efforts to achieve that objective.”
Surge in open warfare
Tuesday’s pre-dawn Israeli strike targeting Ata came hours before another strike attributed to Israel, which targeted a senior Islamic Jihad commander based in Syria. The strikes appeared to be a new surge in the open warfare between Israel and Iranian proxies in the region.
Iran has forces based in Syria, Israel’s northern neighbor, and supports Hezbollah militants in Lebanon. In Gaza, it supplies Islamic Jihad with cash, weapons and expertise. Netanyahu has also claimed that Iran is using Iraq and far-off Yemen, where Tehran supports Shiite Houthi rebels at war with a Saudi-led coalition backing the government, to plan attacks against Israel. Hamas also receives some support from Iran.
Israel frequently strikes Iranian interests in Syria but Tuesday’s attack in Damascus appeared to be a rare assassination attempt of a Palestinian militant in the Syrian capital.
Questions over timing of Israeli strikes
Netanyahu said the operation was approved 10 days in advance and was carried out when the optimal conditions allowed to strike him without causing collateral damage.
Still, some opposition figures suggested the timing could not be divorced from the political reality in Israel, where Netanyahu leads a caretaker government after two inconclusive elections and his chief challenger, former military chief Benny Gantz, is currently trying to build his own coalition government.
Gantz said he had been briefed on Tuesday’s strike in advance, calling it “the right decision,” and
Netanyahu updated his rival on developments through the day, according to the prime minister’s office. But a successful military operation could bolster Netanyahu as he seeks to hold onto power — especially if he is indicted on corruption charges.
Israel’s attorney general is expected to make a decision in the coming weeks, and an indictment would increase pressure on Netanyahu to step aside. Netanyahu has sought to portray himself as the leader best capable of steering the country through its many security challenges.