The 15-member council unanimously adopted a resolution on Tuesday that "urges the Lebanese government to assert its authority in the south, to exert control and monopoly over the use of force and to maintain law and order on its entire territory".
It also pressed Beirut to prevent attacks across the so-called Blue Line, the UN-demarcated border between Lebanon and Israel, while reiterating "its strong support the territorial integrity, sovereignty and political independence of Lebanon within its internationally recognized boundaries".
The council expressed grave concern at the lingering tension along the Blue Line following attacks initiated by the Lebanese Shia force Hizb Allah last November and rocket attacks from Lebanon into Israel last month.
While al-Qaida network in Iraq claimed responsibility for the December rocket attack in an unverifiable statement, Israel and the US both insisted it could not have taken place without the knowledge of Hizb Allah, which faces calls for the disarming of its military wing.
Lebanon's government has been nearly paralysed since December 12, when Hizb Allah and the country's other Syrian-backed Shia movement, Amal, ordered their cabinet members not to participate.
Tension between pro- and anti-
Syrian groups have risen of late
Two weeks ago, the Security Council already urged Beirut to pursue efforts to secure the disbanding and disarming of the militias, notably Hizb Allah, through a broad national dialogue.
Hizb Allah was instrumental in bringing about the withdrawal of Israeli forces from southern Lebanon in 2000 and the group insists its forces must remain there to prevent a new Israeli occupation.
The council meanwhile decided to extend the current mandate of the UN Interim Force in Lebanon (Unifil), which expired on Tuesday, for another six months until 31 July.
Without a vote, the mandate of the 2000-strong UN Interim Force in Lebanon would have expired at midnight.
Although the UN mission has been in place since March 1978, the resolution stressed its "interim nature" and said the council was "looking forward to the early fulfilment of its mandate".
Israel and Hizb Allah regularly
exchange fire across the border
The resolution asked Kofi Annan, the UN secretary-general, to report back within six months on how well Lebanon was doing in "extending its sole and effective authority throughout the south.."
Annan and the council have pressed Lebanon to assert control over the south since Israel pulled out of the region in May 2000, ending 22 years of occupation.
After the Israeli withdrawal, Hizb Allah came to dominate the area, profiting from a power vacuum there to launch sporadic cross-border attacks on Israeli forces in the occupied Shebaa Farms.
Hizb Allah operations often prompt Israeli retaliation in the form of military flights that violate Lebanese air space.
Annan and the council have also been urging the Lebanese government to disarm Hizb Allah, in line with a September 2004 council resolution demanding that all foreign militias on Lebanese soil be disbanded.
But Hizb Allah has refused to do so and last year joined the Lebanese government after a landslide victory in June parliamentary elections.