Witnesses say machine-guns and rocket-propelled grenades were heard from the heavily guarded district of al-Mezze, which hosts several security buildings.
Syrian TV said three “terrorists” and a security force member had been killed.
The UN estimates more than 8,000 people have died in the year-long uprising.
Meanwhile, a team of experts sent by special UN and Arab League envoy Kofi Annan has now arrived in Syria to discuss ceasefire and monitoring plans.
Al-Mezze has previously been the scene of large anti-government protests.
One resident told Reuters news agency there was “fighting near Hamada supermarket and the sound of explosions there and elsewhere in the neighborhood”.
He added: “Security police have blocked several side streets and the street lighting has been cut off.”
Opposition activist Amer al-Sadeq told the BBC’s World Today programme he had spoken to a contact in al-Mezze who reported four blasts within five minutes and then heavy gunfire.
The UK-based Syrian Observatory for Human Rights called the fighting “the most violent of its kind and closest to security centres in Damascus since the revolution began”, adding that 18 government troops had been injured.
The BBC’s Lina Sinjab, in Damascus, says the gunfire continued into Monday morning, with reports saying it has now ended.
The pro-government Ikhbariyah TV station said that in addition to the dead, one gunman had been captured. It put the number of security personnel wounded at three.
In January, the rebel Free Syria Army briefly seized several Damascus suburbs.
The latest incident follows bomb blasts in Damascus and the northern city of Aleppo over the weekend.
The car bomb that exploded in Aleppo on Sunday killed at least two people and injured 30 others.
A day earlier, at least 27 people were reported to have been killed and 97 wounded in two explosions in the capital.
State TV described the blasts as “terrorist” attacks.
However, activists have accused the authorities of staging incidents to discredit opposition groups.
Reuters news agency on Monday reported residents of the eastern city of Deir Ezzor as saying that dozens of tanks had entered the city to try to dislodge Free Syrian Army rebels.
On Monday, a team of experts arrived in Syria to press Mr Annan’s proposals for a ceasefire and monitoring.
In some parts of Syria, rebel fighters, like these in Annan spokesman Ahmad Fawzi told AFP: “There are five people with expertise in peacekeeping and mediation. They will be staying for as long as they are making progress to reach agreement on practical steps to implement Mr Annan’s proposals.”
Meanwhile, the head of the International Committee of the Red Cross (ICRC), Jakob Kellenberger, has travelled to Moscow to meet Foreign Minister Sergei Lavrov and ask the Russian government to press Syria to allow more humanitarian access.
The ICRC says that, in the worst-hit areas, a daily pause in the fighting of at least two hours was needed for the evacuation of the wounded and to allow in food and medicine.
Mr Kellenberger said in Moscow: “Our assessment, unfortunately, is that the humanitarian situation is most likely to deteriorate.”
Russia is a key ally of Syria and, along with China, has thwarted attempts to form a UN resolution condemning the repression.
The BBC’s Daniel Sandford in Moscow says Mr Lavrov is likely to say that while Russia is engaging with Syria, it cannot tell the government there what to do.
Our correspondent says there is some frustration in Moscow with the speed at which Damascus is responding to some initiatives, particularly that of Mr Annan.
President Assad is trying to quell an increasingly armed rebellion that sprang from a fierce crackdown on peaceful pro-democracy protests a year ago.
He insists his troops are fighting “armed gangs” seeking to destabilise Syria.
