UNITED NATIONS (AP) ― Key U.N. Security Council members began discussing a possible new resolution Tuesday that demands an end to the violence in Syria, first by government forces and then by opposition fighters, in hopes of overcoming opposition from Russia and China.

Russia and China have vetoed two previous council resolutions, saying they were unbalanced and only demanded that the government stop attacks, not the opposition. Moscow, which has taken the lead, accused Western powers of fueling the conflict by backing the rebels.

The new draft resolution, proposed by the United States and obtained by The Associated Press, tries to take a more balanced approach in an effort to get Russia and China on board, but it was unclear if the new language would be sufficient to satisfy them.

It was discussed behind closed doors by the five permanent council members ― the U.S., Russia, China, Britain and France ― along with Morocco, the Arab representative on the council.

U.S. Ambassador Susan Rice appeared downbeat as she left the meeting, telling reporters: “I don’t think you should expect anything specific.”

In a statement later, Rice said the discussions focused on “whether there is any possibility of reaching agreement around a potential text that would demand an end to the violence in Syria and demand immediate humanitarian access.”

Her statement made clear that Western supporters of a U.N. resolution don’t want to formally introduce the U.S. draft if it’s going to face a third veto.

“If and when it seems there is a basis for a meaningful and viable text, we will propose one to the full Security Council,” Rice said.

She said there would be further talks but gave no date.

Tuesday’s elections in Russia, which returned Vladimir Putin to the presidency, dampened hopes Moscow would soften its stance on Syria.

Russia’s Deputy Foreign Minister Sergei Ryabkov defended his country’s position on Syria, its closest Mideast ally, and told reporters in Moscow on Tuesday that the council should “seek compromise, stimulate negotiations and a political process.”

After Tuesday’s closed discussion of the U.S. draft, Russia’s U.N. ambassador had no comment. China’s U.N. Ambassador Li Baodong, asked about a new resolution, said “we are still working on that.”

Morocco’s U.N. envoy Mohammed Loulichki called the atmosphere “promising,” but added that no date has been set for another meeting on the draft.

The U.S. draft demands that the Syrian government comply with the Arab League plan of action adopted Nov. 2 and immediately cease all violence, release all detainees, and return all Syrian military and armed forces to their original barracks.

Immediately after these measures are implemented, the draft resolution calls on “the armed elements of the Syrian opposition to refrain from all violence.” This “call” is weaker than the “demand” on the government.

The U.S. draft condemns human rights violations by the Syrian government, without a similar condemnation of opposition attacks.

It mentions past Arab League decisions, which include demands that Syrian President Bashar Assad hand over power to his vice president.

The draft deplores “the rapidly deteriorating humanitarian situation” and demands unhindered access for humanitarian organizations, the Arab League, and Arab and international media.

It also welcomes the appointment of former U.N. secretary-general Kofi Annan as the joint U.N.-Arab League envoy “as part of the continuing efforts aimed at immediately bringing an end to all violence and human rights violations, and promoting a peaceful solution to the Syrian crisis.” It asks Annan to work with the Syrian government, other parties in Syria and other countries to fully implement the resolution.