Fresh clashes between Israel and the Iran-backed Lebanese Hezbollah along the shared border on Wednesday signified the danger of a widening war in the region.

Israeli shelling hit southern Lebanese towns in response to a fresh rocket attack by powerful armed group Hezbollah, as cross-border violence extended into a fourth day.

Hezbollah said it had fired precision missiles at an Israeli position in response to the killing of its members in Israeli shelling earlier this week, pledging "decisive" responses to attacks on Lebanese territory, especially deadly ones.

The Israeli military said it was attacking Lebanon after one of its northern positions near the Israeli town of Arab al-Aramshe was targeted with anti-tank fire on Wednesday.

It did not immediately provide details on casualties.

A Lebanese security source said Hezbollah fired two precision missiles into Israel, which the group considers its sworn enemy.

Residents of the southern Lebanese town of Rmeish said Israeli shelling hit nearby. A security source told Reuters that Israeli artillery rounds were hitting the rocket launch point around Dhayra, across from Arab al-Aramshe.

Local Lebanese television station al-Jadeed broadcast images of plumes of white smoke billowing out of a wooded region near some homes and farmland in Dhayra.

Hezbollah and Palestinian faction Hamas both claimed attacks from Lebanon on Tuesday. Lebanon's Hezbollah fired a guided missile at an Israeli tank, posting a video of its destruction, and Hamas said it launched a salvo of rockets into Israel.

The outbreak of violence along the border came after Hamas launched a deadly attack against Israel at the weekend, with Israel unleashing a bombing campaign against Gaza.