The Syrian army is reported to have regained control of some Damascus suburbs recently held by rebel forces.
Russia has said it will block a draft UN Security Council resolution calling for a transfer of power in Syria because it “leaves open the possibility of intervention” in Syria’s affairs.
The US, the UK and France are lobbying on behalf of the Arab League’s draft text, which calls for President Bashar al-Assad to hand power to a deputy.
The White House said Mr Assad had lost control of Syria, adding “he will go”.
But Russia’s Deputy Foreign Minister said the text was “not balanced”.
Meanwhile, fighting in Syria continued as government troops bombarded the central city of Homs. Heavy machine gun fire was reported in the restive Bab Amr district.
At least 225 tank shells were fired at the suburbs of Damascus, activists said.
The Local Co-ordination Committees, a network of anti-government groups, said 58 people were killed on Monday.
Their claims could not be independently verified, as the the BBC other international media are severely restricted inside Syria.
Earlier, reports said the Syrian army had regained control of some Damascus suburbs recently held by rebel forces.
Moscow, which has maintained its ties to Damascus, has so far resisted moves for a UN resolution condemning the violence in Syria. Russia has a naval base in the country and supplies arms to Syria.
Western states hope Tuesday’s Arab League briefing to the Security Council can break the impasse over Syria. US and European foreign ministers will be present to demonstrate their support for the Arab plan, which they want the council to endorse.
But the Russians have met this combined offensive with rejection. Keen to protect a thriving arms trade with Syria, they have complained about the resolution’s call to stop the flow of weapons to the country (although it doesn’t impose an arms embargo).
But the critical issue is the fate of Bashar al-Assad, Russia’s closest Arab ally. The Arab peace plan calls on him to delegate power to a deputy. For the Russians this is regime change by another name.
So the bottom line is: can there be a compromise between Arab and Western states on the one hand, which says there there is no solution with Assad, and Russia on the other, which insists there is no solution without him.
“The current Western draft… certainly cannot be supported by us,” Deputy Foreign Minister Gennady Gatilov told the Interfax news agency.
Mr Gatilov said the draft was “not balanced” and “leaves open the possibility of intervention in Syrian affairs”.
The White House said it supported a political solution to end the violence in Syria. However, spokesman Jay Carney said President Assad had lost control of his country and his regime would fall.
France says 10 of the 15 countries on the Security Council now support the Arab League text. A minimum of nine council members must lend their backing in order for a resolution to be put to a vote.
However, Russia – as one of the five permanent council members – can veto any proposed resolution.
The BBC’s Barbara Plett, at the UN, says Russia views the resolution as a first step towards regime change.
The UK has urged Moscow to reconsider its opposition.
“Russia can no longer explain blocking the UN and providing cover for the regime’s brutal repression,” said a spokeswoman for Prime Minister David Cameron.
On Monday, Russia also offered to mediate talks between the Syrian government and the opposition – a suggestion the opposition rejected out of hand.
The Syrian government has rejected the Arab League plan, which would see Mr Assad’s deputy forming a national unity government within two months.
The prime minister of Qatar and the secretary-general of the Arab League are also going to New York to seek support for the draft text. Qatar heads the League’s committee dealing with the Syrian crisis and has previously called for Arab countries to send troops into Syria.
On Saturday, the Arab League announced it was suspending its month-old monitoring mission in Syria because of an upsurge of violence.
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Reports from Damascus say residents in some areas heard the sound of bombing in the early hours of the morning.
Heavy fighting has taken place in the eastern suburbs for several days.
Over the weekend, troops loyal to Syrian President Bashar al-Assad launched an offensive targeting several areas under the control of the rebel Free Syrian Army (FSA).
They retook control of the suburb of Ghouta, with activists saying the FSA had beaten a “tactical” retreat.
On Monday, the Syrian army held funerals for 22 of its members killed in the previous 24 hours. The BBC’s Jim Muir, in neighbouring Lebanon, says on average 20 members of the security forces are being killed each day.
Reports have emerged suggesting security forces may have killed senior army defector Lt-Col Hussein Harmoush, one of the first military officers to publicly declare his opposition to Mr Assad last year.
However, the Free Syrian Army, many of whose members are based in Turkey, said they could not confirm the death.