Secretary of State Hillary Rodham Clinton condemned “in the strongest possible terms” the escalation of Syrian government attacks on opposition protesters and said she would voice American concerns at a U.N. Security Council meeting on the subject Tuesday.

The intensified diplomacy came amid ongoing fighting between government and opposition forces on the outskirts of Damascus. In skirmishes throughout Monday, forces loyal to President Bashar al-Assad appeared to have pushed back rebel soldiers fighting for the Free Syrian Army from districts on the eastern edge of the capital.

The Security Council is due to discuss an Arab-backed resolution calling for Assad to step aside during a political transition, a plan similar to the Arab-backed initiative that eased Yemeni President Ali Abdullah Saleh from power. Foreign ministers from Britain and France will attend the meeting, along with Clinton.

Russia already has indicated it would not support the proposal and would reject a Western-backed resolution calling for additional economic sanctions against Syria.

Moscow has offered to mediate talks between the Assad government and the Syrian opposition, and Russian officials said Monday that the government had agreed to participate. But the Syrian National Council, a leading opposition group, rejected the proposal over the weekend.

Burhan Ghalioun, the Paris-based leader of the opposition Syrian National Council, said that the only acceptable resolution is one that condemns Assad’s “crimes against humanity” and brings his departure.

Ghalioun, in New York for the Security Council session, called on Russia, “which has long, historical ties with the Syrian people” to prevent Assad from “exploiting” that relationship. “Any U.N. resolution that does not put an end [to Assad] will not provide the proper environment for peaceful political negotiations” but “would further lead us to the edge of civil war,” he told reporters.

Syria is Russia’s only remaining ally in the Arab world, where it has seen its influence shrink abruptly. Moscow reacted angrily to the Western intervention in Libya, which it said was an illegal extension of a U.N. mandate to protect civilians. Russians officials have said they would not permit similar outside action in Syria, which is far closer to its borders. Western powers and NATO have said they have no intention of military intervention there.

The Obama administration sees little benefit in a Security Council vote that Russia and possibly China would veto. U.S. officials have tried to persuade Moscow to participate in a plan to ease Assad from power, arguing that his departure is only a matter of time and that Russia’s influence can best be preserved in a plan to stem the violence.

On Monday, State Department spokeswoman Victoria Nuland said Clinton has been “trying to get [Russian] Foreign Minister [Sergey] Lavrov on the phone for about 24 hours. “That’s proven difficult,” Nuland said. “He’s in Australia and apparently unavailable.”

In New York, Security Council negotiators worked behind closed doors on a draft resolution, but diplomats said they made little headway on the thorniest issues, including increased sanctions and the call for Assad to step aside. U.S. officials said a vote on the resolution was unlikely Tuesday.

Clinton, in a statement released by the State Department, said that the U.N. Security Council “should send a clear message of support to the Syrian people: We stand with you.

“The longer the Assad regime continues its attacks on the Syrian people and stands in the way of a peaceful transition,” she said, “the greater the concern that instability will escalate and spill over throughout the region.”