JERUSALEM — In a surprise airstrike before dawn on Tuesday, Israeli forces killed a senior commander of the Palestinian Islamic Jihad militant group in the Gaza Strip, setting off waves of retaliatory rocket attacks that immediately raised fears of an escalating new conflict.

The timing of the attack, after a period of relative calm along the border and amid a protracted, high-stakes negotiation over who will lead Israel’s next government, led some critics of Prime Minister Benjamin Netanyahu to charge that it was politically motivated. Mr. Netanyahu insisted that the timing was dictated by Israel’s security chiefs, whose recommendation he had merely endorsed.

Israel described the Gaza commander, Baha Abu al-Ata, as a “ticking bomb” who was “responsible for most of the Palestinian Islamic Jihad’s activity in the Gaza Strip.” Islamic Jihad said that the commander’s wife, Asmaa Abu al-Ata, was also killed in the 4 a.m. missile strike.

Before 6 a.m., militants in Gaza began firing barrages of rockets toward southern and central Israel from the Palestinian coastal enclave. Islamic Jihad called the Israeli strike “a declaration of war against the Palestinian people” and said, “Our response to this crime will have no limits.”

Schools were closed in the Tel Aviv metropolitan area as air-raid sirens blared and Iron Dome missiles intercepted dozens of rockets. Tens of thousands of Israelis took cover in bomb shelters.

Islamic Jihad also blamed Israel for another missile attack at dawn on Tuesday on the Damascus home of Akram al-Ajouri, describing him as a member of the group’s political bureau in Syria.

Mr. al-Ajouri was reported to have survived. Sana, the official Syrian news agency, reported that a son of Mr. al-Ajouri and another person were killed. Mr. al-Ajouri is said to be the direct superior of Mr. Abu al-Ata. The Israeli military would not comment on the Damascus airstrike.

The fighting on Tuesday created an awkward situation for Hamas, the larger Islamic militant group that rules the Gaza Strip. While Hamas functions as the local government, with a strong political base, Palestinian Islamic Jihad, which has fewer followers and no responsibilities except to its patrons in Iran, has taken a harder line toward Israel.

Hamas has tried for months to enforce informal cease-fire understandings with Israel — which Palestinian Islamic Jihad has often disrupted with rogue rocket or sniper attacks — in return for cash from Qatar. It now has to decide whether to raise the stakes by joining the group in avenging Mr. Abu al-Ata’s death, or to stand down in hopes of restoring calm.

Hamas said that it, too, mourned Mr. Abu al-Ata’s death and that his killing would not go unpunished, but the group stopped short of saying it would join the fighting.

The Israeli military said Mr. Abu al-Ata was to blame for rocket fire on Nov. 1 and in August, and said he was being closely monitored recently because he was planning a specific new attack against Israel.

His name had cropped up frequently in the reporting of Israeli military correspondents — which an army spokesman, Lt. Col. Jonathan Conricus, said was no accident, and was meant as a warning.

But some Israeli analysts suggested that an incident on Sept. 10, a week before the last Israeli election, may have sealed Mr. Abu al-Ata’s fate: When Mr. Netanyahu made a campaign stop in Ashdod — at a location announced in advance, breaking with customary security precautions — a rocket attack sent the prime minister and his entourage scurrying offstage to shelter.

Amit Segal, a commentator on Israel’s Channel 12, wrote on Twitter that there had been an “invisible laser marker” on the heads of both Mr. Abu al-Ata and his Damascus superior from that moment.

Militant groups in Gaza have clashed with Israel several times in recent years, with the last deadly conflagration taking place over several days in May. A devastating war in the summer of 2014 lasted 50 days and ended with a fragile cease-fire that has since been broken many times.

Targeted strikes against militant leaders have led to war before, and Israel has sworn them off in the past. In 2012, an Israeli airstrike that killed Ahmed al-Jabari, the Hamas military commander at the time, became the opening shot of an eight-day war.

Colonel Conricus said the attack on Tuesday was timed to minimize the chance of other deaths or injuries.

Some 190 rockets were fired on Israel over the course of the day. Dozens were intercepted by air-defense systems, the military said. At least one man was wounded by shrapnel, officials said, but most casualties were minor and involved people hurt as they raced to shelters or treated for panic or fainting.

Gaza health officials put the casualties there at 10 dead, eight of them militants, and 45 wounded.

Israel refrained for several hours from additional strikes, saying it wanted to avoid an escalation, though it struck what it said were two Islamic Jihad operatives preparing to launch a rocket around 11 a.m.

But with rocket launches continuing, Israel began more broadly attacking Islamic Jihad targets in the early afternoon, announcing the strikes on Twitter with the hashtag #JiHadEnough.

Giora Eiland, a retired Israeli general and former national security adviser, said he believed that the Damascus attack was also carried out by Israel, and said that Islamic Jihad personnel in Syria had a direct connection with Iran and gave instructions to the group’s members in Gaza.

In the hours after the attack, masked militants of Islamic Jihad surrounded the two-story building where Mr. Abu al-Ata and his wife were killed. It is in Shejaiya, a neighborhood east of Gaza City that saw fierce battles during the 2014 war.

Mutassem Hilis, 23, a university student and a neighbor of the Abu al-Ata family in Shejaiya, said he was woken up by the blast, came out of his building and saw Mr. Abu al-Ata’s body on the sidewalk. One of Mr. Abu al-Ata’s young sons lay injured on the ground and was later driven off to the hospital, he said. The body of Mr. Abu al-Ata’s wife was found in a school opposite the family house.

Within Israel, the violence Tuesday occurred in a moment of heightened political tension, as Mr. Netanyahu fights for his political life. He is leading a caretaker government after two elections, in April and September, ended inconclusively. He also faces a looming indictment in three graft cases, possibly by the end of this month.

Benny Gantz, a centrist former Israeli army chief of staff who defeated Mr. Netanyahu in the September election, now is seeking to form a government and possibly force Mr. Netanyahu from power for the first time in a decade.

Mr. Gantz and others in his Blue and White party expressed support for the Gaza strike, about which he said he had been briefed in advance. He called it “a correct decision tonight for the security of Israel’s citizens and the residents of the south.”

But other Netanyahu opponents charged that the Gaza strike was aimed mainly at aiding the prime minister’s bid to stay in power.

Omer Barlev, a Labor Party legislator, said Mr. Abu al-Ata had been in the military’s sights for a long time, adding: “Why did Netanyahu change his position now?”

And the leader of the mainly Arab Joint List, Ayman Odeh, wrote on Twitter: “A cynical man who lost two consecutive elections will leave only scorched earth in a desperate attempt to remain in office.”

Tacitly acknowledging the need to address those allegations, Mr. Netanyahu appeared publicly alongside Israel’s military and internal-security chiefs. He said they had both recommended killing Mr. Abu al-Ata, and that his Cabinet had authorized it 10 days ago.

“We tried to prevent his activity in various ways, but without success,” said Lt. Gen. Aviv Kochavi, the army chief of staff, explaining his recommendation to attack Mr. Abu al-Ata.

In rare public remarks, the chief of the Israel Security Agency, Nadav Argaman, said Israel had been tracking Mr. Abu al-Ata’s movements for days as he moved from safe house to safe house. “He acted like a wanted man,” Mr. Argaman said.

With Mr. Gantz running out of time to form a government, meanwhile, the flare-up, and his support for the government’s actions, appeared to raise the likelihood of a unity government in which he would join forces with Mr. Netanyahu, perhaps even with Mr. Netanyahu remaining prime minister for a limited period. The two met later Tuesday for what was described as a “security update.”

Avi Benayahu, a former army spokesman, wrote on Twitter that Tuesday’s fighting amounted to “concentrated baking powder for a national unity government.”

“Add in the early tip-off Gantz received about the action and the unreserved support for the operation from Blue and White leaders,” he added, “and you have a perfectly baked cake ready for eating.”

Isabel Kershner and David M. Halbfinger reported from Jerusalem, and Iyad Abuheweila from Gaza City. Ibrahim El-Mughraby contributed reporting from Gaza City.