At least four fighters and a security guard were killed during the incident on Friday, an interior ministry official told Syria's state run news agency, SANA.
The fighters were reportedly spotted in a building in central Damascus' Ummayad Square by a police patrol, which then opened fire.
Fayez al-Sayegh, director general of Syria's state-run radio and television services, said the clashes erupted at 6am local time (0300 GMT) when a "group of extremists" tried to storm deserted buildings near the country's state-run radio and television complex.
Initial reports suggested that the media building itself was being attacked.
However, Emad Fawzi al-Shaaibi from Syria's strategic research centre told Aljazeera that it seemed the attackers wanted to use the deserted buildings near the media centre as a base to attack other buildings nearby.
Ummayad Square houses several state buildings, hotels and security installations.
Several attackers, all reportedly Syrian, were wounded and captured.
It was not immediately known whether the attackers belong to the Islamist group Jund al-Sham that has clashed with Syrian security forces on several occasions.
In March, Syrian anti-terrorist forces killed a top Jund al-Sham member and his bodyguard during a clash northwest of Damascus.
In December, Syrian security forces also found caches of arms and explosives in Damascus and a bombmaking factory in the city of Aleppo.
Syria has been under pressure from the US to clamp down on Islamist extremists after US authorities alleged that fighters were using Syrian territory to attack US forces in Iraq.