Rebels fought gun battles with government forces in Damascus, in the most violent clashes Syria's capital has seen since the start of the year-old revolt against President Bashar al-Assad.
In a fresh effort to form a united international front on the mounting crisis, France circulated a Western-drafted statement for the U.N. Security Council deploring the turmoil and backing peace efforts by U.N.-Arab League envoy Kofi Annan.
Britain's U.N. envoy said he hoped the statement would be adopted on Tuesday and U.N. Secretary-General Ban Ki-moon called for international unity and unity on the Security Council.
The situation has reached an unacceptable or intolerable situation, Ban told an audience in Indonesia during a visit to Southeast Asia.
I have seen hope that international community will continually speak in one voice and particularly the Security Council I hope will be able to be united so they can speak in one voice, Ban said.
Piling further pressure on Syria's government, long-term Damascus ally Russia also urged Assad and his foes to agree to daily truces, backing an initiative from the International Committee of the Red Cross to reach the wounded.
But neither government forces nor armed rebel movements showed any sign of bowing to calls for restraint.
The clashes in Damascus on Monday came just two days after two car bombs killed at least 27 people in the heart of the city, in a sign that the capital, once apparently immune to the bloodshed, might be starting to sink into the mayhem.
The fighting near the centre of Assad's power base appeared to be an attempt by rebels to show they still pose a serious challenge after being forced out of strongholds in recent weeks.
The United Nations says more than 8,000 people have died in 12 months of turmoil. The government says about 2,000 members of the security forces have been killed by foreign-backed terrorists.
Reports from Syria cannot be independently verified because authorities have barred access to rights groups and journalists.
Moscow and Beijing have twice vetoed U.N. Security Council resolutions that condemned Syria's year-long assault on rebels.
But Russia's foreign ministry called on both Damascus and the armed opposition to agree without delay to daily humanitarian pauses after ICRC President Jakob Kellenberger held talks with Foreign Minister Sergei Lavrov on Monday.
The statement circulated at the Security Council would not be a formal resolution, which carries legal weight, but rather a presidential statement, which is generally non-binding but still needs unanimous backing.
Veteran diplomat Annan dispatched a team of five experts to Damascus on Monday to discuss his proposals to deploy international monitors in Syria to try to stem the bloodshed.
(Additional reporting by Dominic Evans in Beirut, Steve Gutterman in Moscow and Louis Charbonneau at the United Nations; Writing by Crispian Balmer and Matthew Bigg; Editing by Ron Popeski)