Another brief flare-up a month ago, during the Muslim holy month of Ramadan, took place after an Israeli police raid in Jerusalem on the Aqsa mosque compound, a revered site known to Jews as Temple Mount. That prompted Palestinian armed groups in Gaza as well as militias in Lebanon — led by Hamas, according to the Israeli military — to fire barrages of rockets at Israel.

Israel struck back at the militias in southern Lebanon, as well as at Hamas military sites in the Gaza Strip.

But far-right members of the Israeli governing coalition complained that Israel’s response had been too weak, and the ultranationalist minister of national security, Itamar Ben-Gvir, demanded that Israel take more aggressive steps, including resuming its policy of targeted assassinations of militant leaders.

Mr. Netanyahu leads a right-wing governing coalition that includes two far-right parties. But the previous government, under former prime minister Yair Lapid, a centrist, also carried out missile strikes in Gaza, in August, that killed two senior Islamic Jihad commanders and more than 40 other Palestinians, including 15 children, during three days of fierce cross-border fighting.

The Israeli military said on Tuesday that Mr. Bahitini, one of the militants killed in the latest strikes, had taken over the position of one of the militants killed in August, replacing him as the Islamic Jihad commander of the northern region of the Gaza Strip.

Mr. Gallant, the Israeli defense minister, said in a Twitter post before dawn on Tuesday that the military and the Shin Bet, Israel’s domestic security agency, had “precisely carried out their mission against the leadership of the Islamic Jihad in the Gaza Strip. Any terrorist who harms the citizens of Israel will regret it. We will pursue and catch up with our enemies,” he added.

Reporting was contributed by Iyad Abuheweila from Gaza City; Hiba Yazbek and Myra Noveck from Jerusalem; and Gabby Sobelman from Rehovot, Israel.