The proposed measure said the offensive by Haftar's Libyan National Army (LNA) "threatens the stability of Libya and prospects for a United Nations-facilitated political dialogue and a comprehensive political solution to the crisis".
The council "demands that all parties in Libya immediately de-escalate the situation, commit to a ceasefire, and engage with the United Nations to ensure a full and comprehensive cessation of hostilities throughout Libya," the draft says.
Dozens of people have been killed and more than 18,000 displaced since fighting broke out on April 4.
Britain circulated the text late on Monday and a first round of negotiations is to be held later on Tuesday, diplomats said.
Britain hopes to bring the measure to a vote at the council before Friday, but diplomats said it remained unclear whether negotiations on the measure would wrap up that quickly.
Resolutions adopted by the council are legally binding.
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