Calling for the militia, known as Huthis, to act "immediately and unconditionally," the council's 15 member states will demand the group "withdraw their forces from government institutions. and relinquish government and security institutions," according to a draft of the resolution.
The UN Security Council is due to adopt a resolution Sunday urging the Shiite militiamen behind a power grab in Yemen to step down, release government officials and negotiate, diplomats said.
Yemen has descended into chaos since the Huthis seized Sanaa in September, sweeping into the capital unopposed from their northern stronghold. Despite a UN-brokered deal, they have refused to withdraw their fighters from the city.
The crisis escalated after the militia last month took control of key government buildings, prompting Western-backed President Abedrabbo Mansour Hadi to tender his resignation.
The Huthis must "engage in good faith in the UN-brokered negotiations" being led by UN special envoy Jamal Benomar and "safely release President Hadi, Prime Minister (Khalid Mahfoudh) Bahah, members of the cabinet and all individuals under house arrest or arbitrarily detained."
The member states also alluded to sanctions, expressing their "readiness to take further steps in case of non-implementation," but made no explicit reference to Chapter Seven of the United Nations Charter, which allows for economic and military pressure to enforce council decisions.
Yemen's neighbors Saturday, at a Riyadh meeting of the Gulf Cooperation Council, had urged the UN to evoke Chapter Seven.
According to Western diplomats, Russia, under US and European sanctions over Crimea and eastern Ukraine, was reluctant to vote for sanctions.
The text marks the UN Security Council's first resolution since the Huthis took control of the country, in a power grab that Washington and Gulf countries have described as a coup.
The council was due to adopt the text on Sunday in New York, according to diplomats.
UN Secretary General Ban Ki-moon has warned that Yemen is falling apart and said Thursday that Western-backed Hadi should be restored to power.
The Huthis, who have expanded their presence into central and western Yemen, resumed UN-brokered talks on Monday.