Incident marks third day of cross-border salvoes amid wider regional tensions with Iran but was the first time Hezbollah claimed a direct rocket attack on Israeli territory since 2019.
Israel fired artillery shells into Lebanon in response to rocket attacks by Hezbollah, in a major escalation between the Iran-backed Shia movement and Tel Aviv.
The militant group said it fired a barrage of rockets near Israeli positions close to the Lebanese border as a retaliation for Israeli airstrikes on southern Lebanon a day earlier.
A flare-up along the border this week has seen Israel carry out its first air strikes on Lebanese territory in seven years and Hezbollah claim a direct rocket attack on Israeli territory for the first time since 2019.
But following Friday's exchange Israel said it did "not wish to escalate to a full war".
The United Nations peacekeeping force in the border region, UNIFIL, warned of "a very dangerous situation," and called on parties to "cease fire and maintain calm".
Earlier on Friday, Hezbollah said it fired a barrage of rockets.
In a statement, Hezbollah said it it fired near Israeli positions in the disputed Shebaa farms area, with dozens of rockets.
The Shebaa Farms district is claimed by Lebanon but the UN regards it as part of the Syrian Golan Heights, which Israel has illegally occupied since 1967 and unilaterally annexed in 1981.
Israel said the militant group fired 19 rockets, six of which hit Israeli ground.
Most of the rockets were intercepted by Israel's Iron Dome system, its military said in a statement, and the rest fell in open areas.
There were no immediate reports of damage or injuries.
In a statement, Israel said it sounded sirens before noon in the Golan Heights and Upper Galilee near the Lebanese border.
Villagers stop Hezbollah
In the south Lebanon district of Hasbaya, Druze villagers stopped a truck carrying a multiple rocket launcher used by Hezbollah during Friday's attack, a military source told AFP.
A video widely shared on social media showed angry residents blocking the truck's passage and accusing Hezbollah of endangering civilian lives by launching rockets from close to residential areas.
Hezbollah said the truck was stopped after the group conducted Friday's attack, but said the rockets were fired far from residential areas to ensure civilian safety.
The Lebanese army said it arres ted the four people who had launched the rockets and seized the rocket launcher after it was intercepted by villagers.
Not looking for war: Israel
Israel said it was ready for an "escalation" but played down the prospects of all-out war.
"We believe that neither Hezbollah wants a full-out war, and we definitely do not wish to have a war," an Israeli army spokesman, Amnon Shefler, told journalists.
Tension at a politically sensitive time
Hezbollah has stockpiled thousands of rockets in the south of Lebanon, according to reports.
The rocket attack comes after several days of fire over the border, including rare Israeli air strikes on Hezbollah positions.
Overnight air strikes were a marked escalation at a politically sensitive time.
Israel’s new eight-party governing coalition is trying to keep peace under a fragile cease-fire that ended an 11-day war with Hamas party rulers in Gaza in May.