An Israeli military source confirmed that fire was returned at Hizb Allah targets and "the sources of fire”.
“Israeli aircraft were used in the operation,” he added.
The fighting between the two sides was described as “pretty intense” by another Israeli source who declined to be named. The violence raises fears of a new spiral of violence in the region after a period of relative calm.
Lebanese police reported two Israeli jets fired six air-to-surface missiles at a pair of suspected Hizb Allah positions near the villages of Kfar Shuba and Meri on the Lebanese side of the border.
“These attacks ... were aimed at two army positions in the Har Dov sector (within the Shebaa Farms district)”
Unidentified Israeli military source
Earlier, Hizb Allah fired a number of rockets and mortars at Israeli positions in the area at around 1330 GMT. There were no casualties.
The attack targeted positions with anti-aircraft fire in the Shebaa Farms area which is occupied by Israel, another Israeli security source said.
“These attacks ... were aimed at two army positions in the Har Dov sector (within the Shebaa Farms district) and at the moment we have no reports of casualties or damage,” he said, AFP reported.
The Lebanese resistance group said in a statement that it fired 35 mortar rounds and 107-millimetre rockets at positions in Roueyssat al-Aaalam, Sammaqa and Ramta, on the flanks of Mount Hermon.
The small mountainous enclave, which lies on the borders of Israel, Syria and Lebanon, is claimed by Beirut with the backing of Damascus but occupied by Israel.
Meanwhile, the Germans are trying to negotiate a prisoners' exchange deal between Israel and Hizb Allah. As yet, there has been no breakthrough.
Hizb Allah had been observing an unofficial truce for some three months although it had been punctured by an attack on the Shebaa Farms on August 8.
The new outburst of violence also threatens to further embitter relations between Israel and Syria, which has threatened to attack settlements in the Golan Heights - some five (three miles) kilometres from the Shebaa Farms.