The Iran-backed Lebanese group Hezbollah, a Hamas ally, later said one of its fighters was among those killed. It also said it had carried out several attacks on Israeli military positions at the border in support Palestinians in Gaza, where a week long pause in the fighting ended early on Friday.
The Israeli army said its artillery struck sources of fire from Lebanon and air defences had intercepted two launches. The army also said it struck a "terrorist cell". Sirens warning of possible incoming rockets sounded in several towns in northern Israel, sending residents running for shelter.
Lebanon's state news agency reported that two people were killed by Israeli shelling in the Lebanese border town of Houla, and one person was killed in the village of Jebbayn.
Israeli shelling killed a woman and her 35-year-old son in Houla, Shakeeb Koteich, the head of the town's municipal council, told Reuters, saying both were civilians. Hezbollah later said a "martyr" was killed in Houla.
"A shell landed near the house, and then a second one hit the house," Koteich said by telephone.
Following the eruption of the Hamas-Israel war on Oct. 7, Hezbollah mounted near daily rocket attacks on Israeli positions at the frontier while Israel waged air and artillery strikes in south Lebanon.
It has been the worst fighting since a 2006 war between Israel and Hezbollah, part of an Iran-backed alliance that also includes Hamas. About 100 people in Lebanon have been killed during the hostilities, 80 of them Hezbollah fighters. Tens of thousands of people have fled both sides of the border.
Hezbollah released statements claiming five attacks on Israeli military positions at the border, describing these as "in support of our steadfast Palestinian people ... and its valiant and honourable resistance".
A spokesperson for the United Nations Interim Force in Lebanon (UNIFIL) told Reuters that there had been shelling close to its headquarters near the coastal town of Naqoura, and in Aita al-Shaab also in south Lebanon, in the late afternoon.
Lebanon-based militants from Hamas and the Palestinian group Islamic Jihad have also mounted attacks from Lebanese territory.
"Hezbollah has linked what happens at the border with what happens in Gaza," said Nabil Boumonsef, deputy editor-in-chief of Lebanon's Annahar newspaper.
"All the while the war in Gaza continues Lebanon will remain threatened by the danger of a major escalation."
Senior Hezbollah politician Hassan Fadlallah earlier said the group was vigilant and ready after the Hamas-Israel truce ended.
"In Lebanon, we are concerned in facing this challenge, being vigilant, and always ready to confront any possibility and any danger that may arise in our country," he said.
"No one thinks that Lebanon has been spared from this Zionist targeting or that what is happening in Gaza cannot affect the situation in Lebanon," he said.
(Reporting by Maya Gebeily, Tom Perry, Maggie Fick and Laila Bassam in Beirut and Ari Rabinovitch and Henriette Chacar in Jerusalem; Writing by Tom Perry; Editing by Gareth Jones, William Maclean)
