TRIPOLI, May 31 (Xinhua) -- Libya's UN-backed Prime Minister Fayez Serraj said on Thursday that the Paris meeting held on Tuesday is important for ending the political crisis in his country.

Serraj made the remarks during his meeting with Thomas Waldhauser, commander of U.S. Africa Command, and Stephanie Williams, U.S. charge d'affaires to Libya, in the capital Tripoli.

According to a statement by the prime minister's office, the meeting discussed mechanisms for implementing the initiative at the Paris meeting on Libya, as well as joint efforts against the Islamic State (IS) militant group.

But Serraj admitted the challenges ahead, saying efforts, sincerity and a unified international position are needed to support the implementation of the statement agreed upon at the Paris meeting.

For the U.S. envoy, Williams highlighted a solid ground for direct coordination with Ghassan Salame, the UN special envoy to Libya.

On Tuesday, France hosted a meeting on Libya in Paris which gathered the Libyan parties to end the Libyan political crisis.

In the meeting's final communique, Libyan Prime Minister Fayez Serraj, Khalid al-Meshri, head of the Libyan High Council of State, the eastern-based Parliament Speaker Agila Saleh and the eastern-based army commander Khalifa Haftar pledged "to work constructively with the UN to hold credible and peaceful elections and to respect election results."

The rival Libyan factions also agreed to hold "credible" presidential and parliamentary elections on Dec. 10.

The final communique also stipulated that all parties must accept the results of the elections and provide security for the elections process.