The Shebaa area has been a flashpoint since Israel pulled out of Lebanon

Hezbollah said one of its fighters had been killed "while carrying out his task in the framework of holy war".

Earlier on Tuesday there were also reports that a Hezbollah had fired a Katyusha rocket into northern Israel.

However Hezbollah, Lebanese security services and UN peacekeepers in southern Lebanon all said they knew nothing about the incident.

Hezbollah 'deploying on border'

At the UN in New York, the Israeli Government delivered a letter to Secretary General Kofi Annan, warning that recent attacks against Israeli civilian and military targets could have "alarming consequences on the stability of the region."

The letter from Foreign Minister Shimon Peres urged Mr Annan to intervene immediately and persuade the governments of Lebanon and Syria to take steps to prevent violations of Israel's northern border.

Israel says that in the past two weeks, armed groups have launched several attacks on Israeli military and civilian targets.

Mr Peres also said there is growing evidence that in recent days Hezbollah have started deploying armed men along the "blue line" monitored by the UN separating Israel and southern Lebanon.

A spokesman for Mr Annan said UN monitors are still trying to confirm the reported missile attacks from southern Lebanon.

He said the concern is that a second front of fighting might open up in what is already a very dangerous situation.