Eleven people, including six children, were killed by Israeli strikes on villages across southern Lebanon on Wednesday, a hospital director and three Lebanese security sources said, as Israel said it responded to a Hezbollah rocket attack that killed one of its soldiers.

Hezbollah and the Israeli military have been exchanging fire along the Israel-Lebanon border for more than four months, after the Lebanese armed group launched rockets across the disputed frontier in support of its Palestinian ally Hamas.

A woman and her two children were killed in an Israeli strike on the village of al-Sawana, two security sources said.

A strike on a building in Nabatieh killed four more children, three women and a man, according to the director of the town's hospital, Hassan Wazni, and three other security sources. Seven people were also wounded, Wazni told Reuters.

Four Hezbollah fighters were killed in separate strikes, according to the group and security sources.

Hezbollah did not announce any operations on Wednesday. The head of its executive council said Israel's attacks on Lebanon "cannot pass without a response".

An Israeli government spokesperson told journalists that rocket barrages from Lebanon on Wednesday morning had killed an Israeli soldier, and eight others were hospitalized.

"As we have made clear time and time again, Israel is not interested in a war on two fronts. But if provoked, we will respond forcefully," said spokesperson Ilana Stein.

"The current reality, where tens of thousands of Israelis are displaced and cannot return to their homes, is unbearable. They must be able to return home and live in peace and security."

Stein and Israel's military said the military had responded to cross-border rocket fire from Lebanon.

Israel's military chief Herzi Halevi, who had been meeting the heads of local municipalities in northern Israel on Wednesday, said that despite what he described as achievements against Hezbollah, this was "not the time to stop."

Hezbollah head Sayyed Hassan Nasrallah said in a televised address on Tuesday that his group would only stop its exchanges of fire if a full ceasefire was reached for Gaza.

The cross-border shelling has already killed more than 200 people in Lebanon, including more than 170 Hezbollah fighters, as well as around a dozen Israeli troops and five Israeli civilians. It has also displaced tens of thousands of people in the border areas of each country.