Fresh clashes broke out in the capital while security forces killed at least 16 civilians in violence across the country, according to monitors and activists.
Abu Omar, an activist in Damascus, said security forces were deployed in force in most districts of the capital, especially around Abbasid Square, while they also raided several outlying towns, including Douma and Dmeir.
The Britain-based Syrian Observatory for Human Rights said gunfire was heard in the Qaboon and Barzeh districts, while the Local Coordination Committees, which organises protests, reported shooting around Arnus Square as well.
The security clampdown follows deadly twin suicide car bombings against security buildings in Damascus on Saturday.
It also followed what activists said was a hit-and-run attack in the capital's heavily-guarded Mazzeh neighbourhood on Monday that killed at least three rebels and a member of the security forces.
Elsewhere, four civilians were killed Tuesday as a rocket hit their home in Homs and three others -- a man, woman and their little girl -- in Rastan, both cities in central Syria, the Observatory said.
It also reported civilian deaths in Homs and Hama, also central Syria, Deir Ezzor to the east, and Aleppo in the north, while a soldier was killed in Daraa, southern Syria, and a deserter in the northwestern province of Idlib.
On the diplomatic front, Russian support for a daily humanitarian truce had raised hopes of a breakthrough at the UN Security Council on Syrian crisis but Moscow on Tuesday made it clear its support of any UN statement was conditional.
"We are ready to back the mission of UN and Arab League representative Kofi Annan and the proposals to the government and opposition to Syria," Foreign Minister Sergei Lavrov told reporters in Moscow.
However, the council "should approve them not as an ultimatum."
And he stressed that the proposals Annan made to Syrian President Bashar al-Assad during their meetings in Damascus earlier this month had still not been published and needed to be put up for an open debate at the Security Council.
Lavrov's comments came ahead of a Security Council meeting to discuss the draft which urges Assad and the armed opposition to "implement fully and immediately" Annan's peace plan.
The Western-drafted statement, which France submitted on Monday, says the Security Council will "consider further measures" if nothing is done within seven days of any adoption.
Ahead off the meeting in New York, UN chief Ban Ki-moon warned: "We have no time to waste, no time to lose, because one minute, one hour of delay will mean more and more people dead."
Monitors say a crackdown by the regime on dissent since last March has cost more than 9,100 lives.
The plan of former UN chief Annan includes a halt to the year-long violence, humanitarian access, the release of detainees and withdrawal of security forces from protest cities.
Russia and China have since October twice used their powers as permanent members of the 15-nation council to veto resolutions on Syria. They said the resolutions 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 crisis in Syria.
Her comments followed a meeting between Lavrov and international Red Cross chief Jakob Kellenberger in Moscow on Monday at which they called for a daily humanitarian truce in Syria.
"The two parties call for the Syrian government and armed groups to immediately agree to a daily humanitarian truce to allow the ICRC access to the wounded and to civilians who need to be evacuated," the foreign ministry said.
Amid growing concern at the plight of civilians caught up in an increasingly-armed conflict, a technical mission sent by Annan arrived in Damascus at the weekend for talks on a monitoring operation to end the bloodshed.
Separately, technical experts from the UN and Organisation of Islamic Cooperation are taking part in a Syrian government-led mission to assess the impact of the crackdown on protest hubs battered by security forces.
The mission to 15 cities, on the UN's first such assignment in conflict-strewn Syria, was launched in the flashpoint city of Homs on Sunday.
"The Syrian government's brutal tactics cannot justify abuses by armed opposition groups," said Sarah Leah Whitson, the New York-based organisation's Middle East director.