Still, Russian Ambassador Vitaly Churkin indicated in his address to the council that agreement could still be reached with more negotiation. He said his country found "some of the elements of our text" in the current draft, "and that gives rise for hope."
An earlier proposal on Syria circulated by Russia had been rejected by some Western and Arab nations for not being strong enough. "We hope the council will come to consensus," Churkin said.
Clinton suggested that more negotiation on the text was necessary before a vote later in the week. "We will have a concerted effort over the next days to reach agreement in the Security Council to put forth a resolution that sends a message to President Assad and his regime," she told reporters.
Earlier in the session, the Arab League made a rare call to the council to condemn violence in a fellow Arab country, and adopt its peace plan.
Arab League Secretary-General Nabil Elaraby told the council that the league wanted the Security Council to act "to support our initiative and not to take its place."
"We are attempting to avoid any foreign intervention, particularly military intervention" in Syria, he said. "We have always stressed full respect of the security, sovereignty and territorial integrity of the Syrian people."
British Foreign Minister William Hague called for speedy action.
"How long do Syrian families have to live in fear that their children will be killed or tortured, before the Security Council will act?" Hague asked. "How many people need to die before the consciences of world capitals are stirred?"
In its current form, the resolution demands that Assad halt the crackdown and implement an Arab League peace plan calling for him to hand over power to his vice president. If Assad fails to comply within 15 days, the council would consider "further measures," a reference to a possible move to impose economic or other sanctions.
In his response, Syria's U.N. Ambassador Bashar Ja'afari lashed out at the league, accusing it of acting without consulting the Syrian leadership."How strange it is for us to see some members of the League of Arab States seeking the support of the Security Council against Syria," Ja'afari said. He noted that the Security Council often has voted in support of Israel against Arab-backed measures.
U.N. Secretary-General Ban Ki-moon said Tuesday at a news conference in Amman, Jordan, that he was "encouraged by the League of Arab States' initiative to seek a political solution" to the Syrian crisis.
"It is more urgent than ever to put an end to this bloodshed and violence, to start a credible political solution that addresses the legitimate aspiration of the Syrian people and to protect their fundamental freedoms," Ban said.
Associated Press writer Eileen Alt Powell at the United Nations, and Elizabeth A. Kennedy in Beirut contributed to this report.
Copyright 2012 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.