"A ceasefire must be total," said Leon, wrapping up a three-day visit to the North African nation for talks on ways of ending weeks of fighting in the capital Tripoli and second city Benghazi.
On August 22, the mainly Islamist alliance Fajr Libya (Libya Dawn) seized Tripoli airport south of the capital after weeks of fierce fighting with a nationalist militia.
Three days later Libya's embattled interim authorities said Tripoli was in the hands of armed militias who have since spread their influence across the capital.
Fajr Libya launched an offensive against Warshefana last week, charging that diehard loyalists of slain dictator Moamer Kadhafi are holed up there.
Fajr Libya is one of many militia groups who fought in the 2011 NATO-backed uprising to topple the Kadhafi regime.
The United Nations estimates that the Tripoli fighting has displaced at least 100,000 people, and another 150,000 have fled the country, including many migrant workers.
The UN mission in Libya, UNSMIL, last week reported grave human rights violations during the clashes and Human Rights Watch on Monday said the militias committed "war crimes" against civilians.
"Regarding the political track, there is a general agreement that the only solution is dialogue," he said.
"Everybody agrees that having two parliaments in the country... Is not possible and complicated things," he said.
He stressed that the United Nations recognises only the parliament elected on June 25, describing it as the "sole legitimate representative of the Libyan people".
But that parliament and the Western-backed government linked to it have fled to the eastern city of Tobruk, hundreds of kilometres from Tripoli.
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