The UN Security Council started closed consultations on the measure on Friday morning.
"We hope that tomorrow morning, we can go for a vote and adopt it unanimously," Russia's Ambassador to the UN Vitaly Churkin said on Friday.
The draft resolution endorses the agreement that also commits the Syrian government and the opposition to enter into direct talks at the end of January in the Kazakh capital, Astana.
The talks aim to reach a political solution to put an end to years of Takfiri violence in the Arab country.
The all-Syria ceasefire is holding across the country despite initial instances of violations by foreign-backed militants, a monitoring group and militant sources said.
The ceasefire agreement excludes the most brutal of terror outfits operating in Syria, namely Daesh and Jabhat Fateh al-Sham, formerly known as al-Nusra Front.
The truce was mediated by Moscow and Ankara, which were respectively representing the Syrian government and the anti-Damascus militants.
Ankara has stepped up its cooperation with Moscow recently, prompting speculation that Turkey might be moving away from the United States, which is supporting Kurdish militants in Syria.
Syrian Foreign Minister Walid al-Muallem said the Syrian government believes in Russia as a guarantor of the ceasefire agreement, but mistrusts the Turkish role.
Turkey has illegally deployed troops inside Syria to purportedly fight Kurdish militants and Daesh terrorists, prompting strong condemnation by Damascus. Ankara has long been viewed as a transit route for militants into neighboring Syria, Press TV reported.