BEIRUT, July 1 (AFP) - Just a day after his nomination as Lebanon's new premier, Fuad Siniora is having to grapple with the thorny question of disarming the Hezbollah militia following an outbreak of violence on the volatile border with Israel.

Backed by Damascus and Tehran, the anti-Israel Shiite group that also supports education and social needs for impoverished Shiites, has steadfastly refused to lay down its arms, ignoring a UN call to end militias in Lebanon, which forced out Syria in April.

After fresh violence erupted this week, the UN envoy to southern Lebanon, Geir Pedersen, renewed a call for the government "to extend its control over all of its territory, to exert its monopoly on the use of force and to put an end to all attacks emanating from its territory."

The United Nations, as usual, condemned both sides after Hezbollah killed one Israeli soldier and Israel responded by launching an air raid and shelling a disputed border area this week, but the French UN ambassador was not shy to take it a step further.

"It is clear that the incident was started by Hezbollah," Jean-Marc de La Sabliere said, placing the blame directly on the group Washington has branded a terrorist organisation but the European Union has avoided similarly labeling.

Faced with rising international pressure but well aware of Hezbollah's surge of support following the May-June parliamentary elections, the first anti-Syrian legislative majority since the 1975-1990 civil war finds itself doing a precarious balancing act when it comes to the militant group.

The pro-Syrian Hezbollah coalition, seen by many in Lebanon as the heart of anti-Israeli resistance, scored a landslide win in their southern power base and claimed a clear mandate for anti-Israel guerrillas to keep their weapons in defiance of calls for disarmament.

Given that kind of popularity, the prime minister-elect and his fledgling government must now decide whether to back UN Resolution 1559.

The resolution was drafted by France and the United States to call for the withdrawal of Syrian troops from Lebanon and the disarmament of Hezbollah.

International pressure to comply with the resolution following the assassination of ex-premier Rafiq Hariri eventually forced Syria to end a three-decade military presence.

With its economy in shambles, Lebanon desperately needs the support of Western nations and oil-rich Arab countries and could garner favour by going along with UN calls for "the Lebanese government to make sure that the calm is kept," as Pedersen said Friday.

But not all in the new government think that sending Lebanese forces to the Israeli border, where Hezbollah is installed, is a good idea.

Druze chief and MP Walid Jumblatt said the next cabinet "must ask the Security Council to waive" the clause that calls for Hezbollah to disarm.

However, international law expert Sami Salhab said the government would have a difficult time picking and choosing elements of the resolution to back or reject.

"As a member of the UN, the Lebanese government cannot reject this resolution. It must negotiate with the (Security) Council the methods to apply it or present a new plan for the resolution that takes account of its particular situation."

Observers predict Hezbollah's participation in parliament will lead to even more difficult negotiations within Siniora's government, as Hezbollah shows no sign of willingness to disarm and calls have faded for it to integrate into Lebanese forces.

Salhab believes the timing of this weeks clashes was no coincidence.

After it won support in parliamentary elections, Salhab said: "Hezbollah clearly wants to be in a position of power, which explains Wednesday's new flareup in violence beyond the blue line that marks the border between Lebanon and Israel, just a few days before the new government in formed."

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