Updated at 2:19 p.m. ET: Secretary of State Hillary Rodham Clinton will join British and French foreign ministers at the U.N. Security Council on Tuesday to push an Arab-backed condemnation of Syrian President Bashar Assad's regime.
"The status quo is unsustainable," Clinton said in a statement. "The longer the Assad regime continues its attacks on the Syrian people and stands in the way of a peaceful transition, the greater the concern that instability will escalate and spill over throughout the region."
Arab League Secretary-General Nabil Elaraby and Qatar's prime minister are due to plead with the 15-nation Security Council to back the league's plan for Assad to transfer powers to his deputy to prepare for free elections.
Assad's regime is intensifying an assault against army defectors and protesters. The U.N. has said more than 5,400 people have been killed in violence since March. At least 190 additional people were killed in the past five days.
Updated at 7:40 a.m. ET: Street battles raged at the gates of the Syrian capital on Monday as President Bashar Assad's troops sought to consolidate their grip on suburbs that rebel fighters had taken only a few miles from the center of government power. Syrian forces also heavily shelled the restive city of Homs.
Russia, a U.N. Security Council member and one of Syria's few allies, said President Bashar Assad's government 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 armored vehicles and artillery to beat back rebels who came as close as 5 miles to Damascus.
An activist said the Free Syrian Army - a force of military defectors with links to Syria's divided political 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 neighborhood. "The sound of gunfire is everywhere."
Updated at 4:58 a.m. ET:Troops seized eastern suburbs of Damascus from rebels late on Sunday, opposition activists said, after two days of fighting only a few miles from President Bashar Assad's center of power.
"The Free Syrian Army has made a tactical withdrawal," an activist named Kamal told Reuters by phone from the eastern al-Ghouta area on the edge of the capital. "Regime forces have re-occupied the suburbs and started making house-to-house arrests."
A spokesman for the Free Syrian Army of defectors fighting Assad's forces appeared to confirm that account.
"Tanks have gone in but they do not know where the Free Syrian Army is. We are still operating close to Damascus," said Maher al-Naimi, who spoke to Reuters from Turkey.
Meanwhile, Syria's state news agency reported Monday that a "terrorist" group had blown up a gas pipeline.
The rising bloodshed added urgency to Arab and Western diplomatic efforts to end the 10-month conflict.
In the past two weeks, army dissidents have become more visible, seizing several suburbs on the eastern edge of Damascus and setting up checkpoints where masked men wearing military attire and wielding assault rifles stop motorists and protect anti-regime protests.
Their presence so close to the capital is astonishing in tightly controlled Syria and suggests the Assad regime may either be losing control or setting up a trap for the fighters before going on the offensive.
Activists said earlier on Sunday soldiers had moved into the suburbs at dawn, along with at least 50 tanks and other armored vehicles. At least 19 civilians and rebel fighters were killed in that initial attack, they said.
NBC's Ayman Mohyeldin visits Zabadani, Syria, a once beautiful snowcapped resort town that has been deeply scarred by the recent military crackdown and speaks with members of the anti-regime Free Syria Army.
Fighters had taken over districts less than five miles from the heart of the city. The areas have seen repeated protests against Assad's rule and crackdowns by troops during the uprising.
"It's urban war. There are bodies in the street," said an activist speaking from the suburb of Kfar Batna.
Residents of central Damascus reported seeing soldiers and police deployed around main squares.
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, will discuss the crisis on February 5.
Arab League chief Nabil Elaraby left for New York where he will brief representatives of the U.N. Security Council on Tuesday to seek support for the Arab peace plan.
He will be joined by Qatari Prime Minister Sheikh Hamad bin Jassim al-Thani, whose country heads the League's committee charged with overseeing Syria.
The Syrian government says the country is being attacked by extremists but some civilians say the only armed gangs in the city are the security forces. NBC's Ayman Mohyeldin reports.
Elaraby said he hoped to overcome resistance from Beijing and Moscow over endorsing the Arab proposals.
A Syrian government official said the 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.
The uprising against Assad, which began with largely peaceful demonstrations, has grown increasingly militarized recently as more frustrated protesters and army defectors have taken up arms.
The opposition Syrian Observatory for Human Rights reported 41 civilian deaths across Syria on Sunday, including 14 in Homs province and 12 in the city of Hama. Thirty-one soldiers and members of the security forces were also killed, most in two attacks by deserters in the northern province of Idlib, it said.
State news agency SANA reported the military funerals of 28 soldiers and police on Saturday and another 23 on Sunday.
After mass demonstrations against his rule 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 current battles taking place in and around Damascus may not yet lead to the unraveling of the regime, but the illusion of normalcy that the Assads have sought hard to maintain in the capital since the beginning of the revolution has surely unraveled," said Ammar Abdulhamid, a U.S.-based Syrian dissident.
"Once illusions unravel, reality soon follows," he wrote in his blog Sunday.
Reuters and The Associated Press contributed to this report.