Russia's UN Ambassador Vitaly Churkin said creating a central authority that can work effectively throughout the country is especially important "in light of the terrorist threat" and the presence of fighters from the Islamic State extremist group, also known by the Arabic acronym Daesh.
Libya has been dominated by an array of militias since the 2011 uprising that toppled and killed longtime dictator Moammar Gadhafi.
Western nations view the new government, whose leader arrived in the capital Tripoli last week, as the best hope for ending Libya's chaos and uniting all factions against an increasingly powerful Islamic State affiliate, which has seized the central city of Sirte.
Churkin said "it's good that some progress has been made but the situation in the country ... Continues to be nearly catastrophic."
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The UN needs to continue working to make sure "there is maximum unity among various forces in the country," he said, noting that parliament hasn't yet approved the unity government and some influential groups of people remain opposed.
"They should gradually move, hopefully with the support of all the political forces, to reunite the country and to create a new central authority which will be effectively working throughout the country," Churkin said. "For the international community to help the Libyans fight this terrorist threat there must be central authorities."
"Libyans must know ... That the international community stands behind them and will support them in their quest for stability," he stressed.
Britain's UN Ambassador Matthew Rycroft welcomed "the good news" that the head of the new government, Fayez Serraj, is now in Tripoli. He stressed the importance of "a step-by-step process" supported by the international community to accelerate the establishment of a stable and successful government.