Syria's rebel army says it has launched a full scale offensive to liberate the capital, dubbing the campaign Operation Damascus Volcano.
Fighting in the capital appears to be worsening, with reports that Alawite forces are deploying tanks and helicopter gunships as they fight to regain control of rebel-held areas.
The clashes have now reached Sabaa Bahrat Square - a central site where Assad's regime once staged pro-government rallies to counter the opposition protests that erupted early last year.
"There is no going back. The Damascus battle has priority for us. We have started the operation to liberate Damascus", rebel commander Colonel Qassem Saadeddine said.
The Syrian Alawite government has vowed it will never let Damascus fall into rebel hands, and one Syrian diplomat, who has now defected to the opposition, has warned that president Bashar al-Assad's regime will not hesitate to use chemical weapons on its own people if it finds itself cornered.
Former ambassador to Iraq Nawef Fares says chemical weapons may already have been used.
"There is some information, unconfirmed information of course, that chemical weapons have been used partially in Homs", he said.
"However, I have absolute conviction that if the circle of the people of Syria becomes tighter on the regime, the regime will not hesitate to use chemical weapons".
Reports said helicopter gunships armed with heavy machine guns strafed key Damascus neighborhoods on Tuesday and several blasts shook another district a few hours after rebels had announced their full-scale offensive to take the capital.
From the early hours, "regime forces used helicopters fitted with heavy machine guns to attack the [eastern Damascus] district of Qaboon", the Britain-based Syrian Observatory for Human Rights said.
Witnesses also reported heavy machine gun fire in Sabaa Bahrat Square. Shooting was also reported in Baghdad Street, a main road near the square.
Earlier, the Observatory said rebels and troops clashed fiercely in the neighborhoods of al-Hajar al-Aswad and in al-Midan, which is close to the Old City.
"The army is shelling al-Midan hysterically; the collapsing regime has gone mad", an activist who said he was in al-Midan said via Skype.
The man, who identified himself as Abu Musab, described the shelling as "arbitrary. They have just destroyed the Ghazwat Badr mosque".
"The army has tried to storm the district, but the [rebel] Free Syrian Army (FSA) has stopped them. So they have intensified their shelling. They are shelling everything".
Mr Musab's account could not be independently verified.
As the fighting spreads, residents have begun fleeing Damascus in fear.
Others say they are ready to get out at a moment's notice. One witness says city streets are deserted, with shops and businesses closed and people terrified of what could happen.
The FSA launched the Damascus Volcano offensive on Monday "in response to massacres and barbaric crimes" committed by the regime of president Bashar al-Assad, the FSA's central-Homs Joint Command said.
Colonel Saadeddine, a rebel spokesman from the area, said the "battle for the liberation of Damascus has begun" and warned, "victory is nigh".
He said fighting would not stop until the whole of the capital had been conquered.
"We have transferred the battle from Damascus province to the capital", Colonel Saadeddine said.
"We have a clear plan to control the whole of Damascus. We only have light weapons, but it's enough".
"Expect surprises", he added, without elaborating.
A statement from the rebels described their operation across the country as "the first strategic step towards bringing Syria into a state of complete and total civil disobedience".
An activist in the capital said FSA fighters had blocked an attempt by the army to storm Qaboon.
"The army tried to raid the neighborhood yesterday but the FSA stopped them", said the activist, who calls himself Omar.
He said the army, backed by tanks and low-flying helicopter gunships, randomly pounded the neighborhood with mortars and heavy machinegun fire.
Overnight, troops also targeted an electrical power sub-station in Qaboon, causing huge power cuts.
"We were unable to evacuate the wounded because snipers were in control of the streets", Omar said.
Just before dawn there was a lull, he said, but shops were shuttered in Qaboon and few residents ventured out to shop.
Meanwhile, rebels reportedly made gains elsewhere in Syria, the Observatory said.
"In the province of Homs, rebel fighters took control of all checkpoints in Talbisseh on Monday", the watchdog said.
Talbisseh has been controlled by the rebels for weeks and it now appears the insurgents have been able to overrun troops at checkpoints surrounding the town.
On Monday, a total of 149 people were killed across Syria, including 82 civilians, 26 rebels and 41 soldiers, the Observatory said.
According to the Observatory more than 17,000 people have been killed since the uprising against Assad erupted in mid-March 2011.