At least 30 people were killed in Syria on Tuesday as the UN Security Council discussed the violence and long-time Damascus ally Russia said President Bashar al-Assad had "made a lot of mistakes."
Moscow's comments came as UN-Arab League envoy Kofi Annan and Arab League chief Nabil al-Arabi called for a united international stand on the crisis.
In Geneva, Annan briefed Arabi on the mission in Damascus to urge Assad's government to act immediately on Annan's proposals, "including a cessation of the violence and the killing, and agreement on the modalities of a monitoring mechanism," UN spokeswoman Corinne Momal-Vanian said.
"Both men underscored the importance of a unified message from the international community," she added.
They met as the Security Council discussed a statement on the crisis and as Russian Foreign Minister Sergei Lavrov said Assad had made "a lot of mistakes" since peaceful protests began in March 2011.
Lavrov said Moscow was ready to back a Security Council statement or resolution on Syria as long as it did not include an ultimatum.
Annan's proposals to Assad should be published and properly debated and "the Security Council should approve them not as an ultimatum but with consideration for the work that is ongoing" by the UN-Arab League envoy.
But in an interview on Kommersant FB radio, Lavrov said "we believe that the Syrian leadership responded incorrectly to the very first manifestations of the peaceful protests.
"The Syrian leadership -- despite the numerous promises it has made in response to our calls -- is making a lot of mistakes," said Lavrov.
"And the things that are actually moving in the right direction are coming too late," he added.
Pro-democracy demonstrations that began last March were peaceful, but Assad's regime quickly began cracking down with lethal force, and some 9,100 people are estimated to have been killed since then.
Last week, Lavrov also accused Assad of making errors and moving too slowly on reforms, but Tuesday's comments suggest Russia has been unhappy with his leadership from the early stages of the conflict.
Until now, Russian officials have avoided publicly discussing the possibility of Assad's departure and insisted that any transition from his rule needed to be arranged through political dialogue in Damascus.
But Lavrov hinted on Tuesday that Moscow would not be opposed outright to the idea of Assad being offered safe haven by another country.
"Perhaps that is the case, but that is something for Assad to decide," he said in response to a question about whether Syria's president should step down before being toppled and killed like Libyan dictator Moamer Kadhafi.
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Lavrov said it was up to the West to offer an acceptable way out for Assad, and stressed that Moscow had never discussed the possibility of him coming to Russia.
"People in various Western capitals are calling him a war criminal and declaring that his rightful place is in The Hague," he said, in an apparent reference to the International Criminal Court.
"This means that it is the people making these statements who should be the ones explaining his options (to Assad) -- not us."
Lavrov said direct negotiations could help decide the issue of who might lead Syria "through a transition period for a certain time as was the case in Yemen."
A copy of the Western-drafted statement, submitted by France on Monday and obtained by AFP, does not condemn the violence but expresses "gravest concern" at the deteriorating crisis and "profound regret" at the thousands of dead.
It calls on Assad and Syria's opposition to "implement fully and immediately" Annan's six-point peace plan. It says the council will "consider further measures" if nothing is done within seven days of any adoption.
Since October, Russia and China have twice vetoed resolutions on Syria, saying they were aimed at regime change and that they opposed any sanctions.
Before Lavrow's latest statement on the UN draft, the United States had welcomed what State Department spokeswoman Victoria Nuland termed "an evolution in the Russian public position" on the Syria crisis.
Her comments followed a meeting between Lavrov and international Red Cross chief Jakob Kellenberger on Monday at which they called for a daily humanitarian truce in Syria.
In Damascus, meanwhile, activist Abu Omar said security forces were deployed in force in most districts, especially around Abbasid Square, and reported raids on several outlying towns including Douma and Dmeir.
The Syrian Observatory for Human Rights reported shooting in the Qaboon and Barzeh districts, while the Local Coordination Committees, which organises protests, reported shooting around Arnus Square as well.
The Observatory said at least 30 people, all but two of them civilians, were killed in violence elsewhere across the country.
The Damascus clampdown follows deadly twin suicide car bombings targeting security buildings there on Saturday.
It also followed what activists said was a hit-and-run attack in the heavily guarded Mazzeh neighbourhood on Monday that killed at least three rebels and a member of the security forces.
The foreign ministry blamed the same "deadly hand" behind the wave of attacks in Iraq on Tuesday that killed at least 50 people for the weekend Damascus car bombings.