Russia, a U.N. Security Council member and one of Syria's few allies, said Assad's government had agreed to talks in Moscow to end the Syrian crisis, but a major opposition body rejected any dialogue with him, demanding he step down.
The new fighting and Russian diplomacy came as the Arab League and France prepared to lobby the Security Council to act on a peace plan that would remove Assad from power, in a bid to staunch the flow of blood from Syria's attempt to crush a popular uprising and armed insurgency against Assad.
Activists and residents said Syrian troops now had control of Hamouriyeh, one of several districts where they have used armoured vehicles and artillery to beat back rebels who came as close as 8km to Damascus.
An activist said the Free Syrian Army (FSA) - a force of military defectors with links to Syria's divided opposition - mounted scattered attacks on government troops who advanced through the district of Saqba, held by rebels just days ago.
"Street fighting has been raging since dawn," he said, adding tanks were moving through a central avenue of the neighbourhood. "The sound of gunfire is everywhere."
Rebels, emboldened in their struggle against Assad's forces, are risking heavier clashes and fierce reprisals in an attempt to create "liberated" territories across Syria. In the past three weeks they have taken Zabadani - a town of 40,000 in mountainous near the border with Lebanon - but have been beaten back from the outskirts of the capital.
"God willing, we will liberate more territory, because the international community has only offered delayed action and empty threats," said a lieutenant colonel who had defected to the FSA but declined to be named.
Rebels, emboldened in their struggle against Assad's forces, are risking heavier clashes and fierce reprisals and speak of creating "liberated" territories across Syria. In the past three weeks they have taken Zabadani - a town of 40,000 in mountainous near the border with Lebanon - but their forays near the capital have been beaten back.
"God willing, we will liberate more territory, because the international community has only offered delayed action and empty threats," said a lieutenant colonel who had defected to the FSA but declined to be named.
Russia's Foreign Ministry said Syria agreed to Russian-brokered negotiations over the crisis, but senior members of the council that claims to speak for a fragmented Syria opposition said there was no point in talking to Assad, who must quit.
"We rejected the Russian proposal because they wanted us to talk with the regime while it continues the killings, the torture, the imprisonment," Walid al-Bunni, foreign affairs chief for the Syrian National Council, told Reuters.
The rebels said at least 15 people had been killed as they pulled back in Saqba and Kfar Batna. Activists claim a death toll of more than 100 people in three days of fighting in the districts, which have seen repeated protests against Assad's rule and crackdowns by troops on the 10-month-old uprising.
The escalating bloodshed prompted the Arab League to suspend the work of its monitors on Saturday. Arab foreign ministers, who have urged Assad to step down and make way for a government of national unity, are due to discuss the crisis on February 5.
Syria's state news agency said six soldiers died in a single attack near Deraa in the south and "terrorists" had blown up a gas pipeline. Pipelines have been targeted frequently during the uprising.
The state news agency SANA has reported funerals of more than 70 members of the security forces members since Friday.
Residents of Deraa - where anti-Assad unrest first flared - said firefights between army defectors and government troops killed at least 20 people, most of them government forces.
In Homs, the central Syrian city that has seen heavy attacks by Assad's forces and sectarian reprisal killings, residents said government troops backed with armour fought rebels near its marketplace.
Syria limits access for journalists and the details of events could not be immediately verified.
Arab League chief Nabil Elaraby is to seek support on Tuesday for the Arab peace plan from the U.N. Security Council, which France's foreign minister said, through a spokesman, must act against "crimes against humanity committed by the regime".
Elaraby, who wants to overcome Russian and Chinese objections to the plan, will be joined by Qatari Prime Minister Sheikh Hamad bin Jassim al-Thani, whose country heads the League's committee charged with overseeing the Syrian crisis.
Russia's deputy foreign minister earlier on Monday said Moscow first wanted to hear directly from the observers whom the Arab League sent - a move likely to delay any vote.
A Syrian government official said any Arab League decision to suspend monitoring would "put pressure on (Security Council) deliberations with the aim of calling for foreign intervention and encouraging armed groups to increase violence".
Assad blames the violence on foreign-backed militants.
After mass demonstrations against him erupted last spring, Assad launched a military crackdown. Growing numbers of army deserters and gunmen have joined the protesters in a country of 23 million people regarded as a pivotal state at the heart of the Middle East.
The insurgency has crept closer to the capital. The suburbs, a string of mainly conservative Sunni Muslim towns known as al-Ghouta, are home to the bulk of the 3 million population of Damascus and its outlying districts.
The rebel force said on Monday medicine and blood were running low in field hospitals, some set up in mosques, and that advancing government forces were carrying out mass arrests.
The Damascus suburbs have seen large demonstrations demanding the removal of Assad, a member of the minority Alawite sect, an offshoot of Shi'ite Islam that has dominated the mostly Sunni Muslim country for the last five decades.
Iran, Syria's regional ally and once unconditional supporter of Assad's crackdown, said Assad must be spared foreign interference to enact constitutional reforms, hold an election and carry out other measures floated after months of killing.
"We think that Syria has to be given the choice of time so that by (that) time they can do the reforms," Foreign Minister Ali Akbar Salehi said on Sunday.
Syria has said it will hold a referendum on a new constitution soon, before a multi-party parliamentary election that has been much postponed. Under the present constitution, Assad's Baath party is "the leader of the state and society".
The United Nations said in December more than 5,000 people had been killed in the protests and crackdown. Syria says more than 2,000 security force members have been killed by militants.
On Friday, the U.N. Security Council discussed a European-Arab draft resolution aimed at halting the bloodshed. Britain and France want to put it to a vote next week, and a French diplomat said it had backing of at least 10 members.
Russia and China blocked a previous Western draft resolution in October, and Moscow said it wants a Syrian-led political process, not "an Arab League-imposed outcome" or Libyan-style "regime change".
