For weeks, Israelis have waited in trepidation for a major attack by Hezbollah in retaliation for Israel’s assassination of a senior commander of the Lebanese group in Beirut last month, amid widespread fears that a cross-border escalation could spiral into an all-out regional war.

But much of Israel woke up on Sunday to find that at least for the immediate term, the long-dreaded attack appeared to be over almost before it started.

Both Israel and Hezbollah quickly claimed victories of sorts: Israel for its predawn pre-emptive strikes against what the military said were thousands of Hezbollah’s rocket launcher barrels in southern Lebanon; and Hezbollah for its subsequent firing of barrages of rockets and drones at northern Israel, which the Israeli military said killed a naval officer.

By breakfast time, the two sides were employing the language of containment.

Hezbollah announced that it had completed the “first stage” of its attack to avenge the assassination of the senior commander, Fuad Shukr, and appeared to be calling it a day, at least for now. Israel’s defense minister, Yoav Gallant, said he had spoken with the U.S. secretary of defense, Lloyd J. Austin III, and they had “discussed the importance of avoiding regional escalation,” according to a statement from Mr. Gallant’s office.

Hezbollah’s leader, Hassan Nasrallah, said in a speech on Sunday evening that his group had attacked an Israeli intelligence base, Glilot, just north of Tel Aviv. If the results of the attack on the base turned out to be satisfactory, he said, the militia would rest its case.

If it turned out to be a failure, he added, then Hezbollah reserved the right to respond at a later date.