The council has been in talks on a draft resolution on the truce since February 9 as Syrian government forces have waged a fierce air campaign on the rebel-held enclave of Eastern Ghouta.
"We have not been able to close the gap completely," Swedish Ambassador Olof Skoog told reporters following a closed-door council meeting.
"We will work tonight and hopefully, we will definitely come back tomorrow and we will vote."
"Unbelievable that Russia is stalling a vote on a ceasefire allowing humanitarian access in Syria," Haley posted on Twitter.
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"How many more people will die before the Security Council agrees to take up this vote? Let's do this tonight. The Syrian people can't wait."
More than 460 civilians, including more than 100 children, have been killed in the six-day offensive on the rebel-held enclave, where UN Secretary-General Antonio Guterres said 400,000 Syrians are living in "hell on Earth."
In a concession to Russia, the draft resolution states that the ceasefire will not apply to operations against the Islamic State group or Al-Qaeda, along with "individuals, groups, undertakings and entities" associated with the terror groups.
The text would demand the immediate lifting of all sieges, including in Eastern Ghouta, Yarmouk, Foua and Kefraya and order all sides to "cease depriving civilians of food and medicine indispensable to their survival."
Kuwait's Ambassador Mansour al-Otaibi, who holds the council presidency, said "we are very close" but that there was still no consensus on the draft resolution.