The Israeli military said on Sunday morning that it had conducted overnight strikes in Lebanon, hours after a rocket fired from its northern neighbor killed at least 12 people in an Israeli-controlled town.

Israel blamed Hezbollah, an Iranian-backed Lebanese group that has been attacking Israel in solidarity with Gaza, for Saturday’s deadly rocket attack. Hezbollah has denied it was responsible. The Israeli strikes appeared to stop short of a major escalation, amid fears that the rocket launch would prompt all-out war.

The Israeli military said it had chiefly targeted places in Lebanon that it has often hit in the past, mostly close to the border with Israel or surrounding the southern port of Tyre. It reported one strike in the Bekaa Valley, roughly 60 miles to the north, where it has been striking less frequently since February.

Still, there were strong expectations on Sunday morning that Israel still might mount a bigger response. That, analysts fear, could tip the low-level hostilities between Israel and militias led by Hezbollah into more intense conflict. For months, as Israel has fought Hamas in Gaza, it has also been trading fire with Hezbollah.

Israeli Prime Minister Benjamin Netanyahu, who had traveled to the United States, was set to return home on Sunday after cutting his trip short. Overnight, his office said that he would convene a meeting of senior government ministers immediately upon arrival in order to discuss Israel’s response, suggesting that the main Israeli retaliation was yet to come.

“Hezbollah will pay a heavy price which it has not paid up to now,” Mr. Netanyahu’s office said in an overnight statement.

The rocket attack on Saturday hit an Arab town in the Golan Heights, a territory once held by Syria that was captured by Israel during the Arab-Israeli war of 1967.

Israel annexed the territory in 1981, a move that was not recognized by most of the world. Decades later, President Donald J. Trump recognized Israeli sovereignty there, but most countries consider it occupied territory.

Roughly 20,000 Druse Arabs live in the Golan Heights, including in the town hit by the rocket; some still consider themselves Syrian, refusing Israeli citizenship. Jewish Israelis began settling the territory after 1967, and more than 20,000 now live in the area.