The United States said, however, it was important that the 15-member council does not harm efforts under way in Cairo to broker a truce between Israel and Palestinian Hamas militants in Gaza.
The Security Council held heated closed-door negotiations on a possible statement, but diplomats said a sticking point was that the text did not mention Hamas missile attacks on Israel. Israel said it was these attacks that prompted its major offensive against the militants in Gaza.
Council members were consulting with their capitals on the draft statement, which needs to be approved by consensus, but several diplomats said it was unlikely an agreement would be reached by a Tuesday morning deadline.
Russia's U.N. envoy Vitaly Churkin said that if the council could not agree, he would put a resolution - a stronger move by the council than a statement - to a vote on Tuesday to call for an end to the violence and show support for regional and international efforts to broker peace.
"One member of the Security Council, I'm sure you can guess which, indicated ... they will not be prepared to go along with any reaction of the Security Council," Churkin said earlier in a thinly veiled reference to the United States.
"Somehow, allegedly, that could hurt the current efforts carried out by Egypt and the region," he said.
A resolution is passed when it receives nine votes in favor and no vetoes by the five permanent council members - Russia, China, Britain, the United States and France. Some diplomats said a vote on the Russian resolution would likely be tight and could force a veto by the United States.
The Security Council is generally deadlocked on the Israeli-Palestinian conflict, which U.N. diplomats say is due to the United States' determination to protect its close ally Israel. The council held an emergency meeting on Wednesday to discuss the Israeli strikes on Gaza but took no action.
U.S. Ambassador to the United Nations, Susan Rice, said the United States would support a council statement if it "advances the goal of supporting an agreed cessation (of violence)."
"We think it's vitally important that this council by its action or non-action is reinforcing the prospects of an agreed cessation (of violence) and not doing anything that could undermine that prospect or run counter to it," Rice said, referring to the truce negotiations in Cairo.
"That is our principal objective in these discussions," she told reporters.
Palestinian U.N. observer, Riyad Mansour, said the council cannot "remain on the margin."
"We emphasized the urgency of the Security Council to shoulder its responsibility and to stop this aggression against our people," Mansour told reporters after Monday's negotiations.
Council diplomats, who did not want to be identified, said the United States' U.N. delegation had been instructed by Washington not to engage in consultations on a statement by the Security Council.
France, Germany and Britain submitted amendments to the draft Security Council statement earlier, diplomats said, but Churkin said too many changes had been proposed.
"Unfortunately it looked like a little bit of a filibustering attempt. Maybe I am mistaken, maybe it's just a laid-back attitude in a situation where we cannot afford procrastination," Churkin told reporters after consultations.
One council diplomat described the filibustering accusation as "utter nonsense."