The UK has drafted a resolution at the UN Security Council and presented it to member states calling on all Libyan sides to cease their fire in Tripoli.
Diplomatic sources said the UK resolution calls on all sides to cooperate with the UNSMIL and its Head Ghassan Salame to reach a ceasefire across Libya.
The resolution can only pass if 9 out of 15 approve it, provided that none of the five permanent member states votes it.
No date has been given yet for the voting process on the resolution.
The UK ambassador at the UN Security Council told reporters on Monday that Britain hopes the resolution gets approved.
Clashes in southern Tripoli areas continue between Khalifa Haftar's forces and Libyan Army forces under the command of Presidential Council, with documented use of heavy weapons to target residential areas and public institutions by Haftar's forces.