The clash, on Monday, left one policeman dead and two rebels in custody, the state-run SANA news agency said.
SANA, quoting an unidentified Information Ministry official, said the group was made up of former bodyguards of Saddam. But it was unclear if any of those detained were aides to the former Iraqi leader.
The Syrian authorities have said more details will be provided about the group, once it detains the rest of its members, Aljazeera's correspondent in Syria, Abd al-Hamid Tawfiq, reports.
The fighting that took place on a mountain overlooking the capital marked the second day of clashes within Syria and related to the fighting in neighbouring Iraq.
On Sunday, Syria had claimed it was cracking down on insurgent groups - a persistent US demand - and announced its forces had killed an Arab near the Lebanese border and arrested 34 other foreigners.
Syria has been under intense pressure to crack down on such suspected rebels, who the United States and Iraq claim are using Syrian territory to infiltrate into neighbouring Iraq to fight US-led forces.
Monday's battle erupted early morning on Qassioun mountain that overlooks Damascus and is about 3km southwest of the capital.
The Syrian government claims it
is cracking down on insurgents
Police Major Ahmad Hijazi was killed in the clashes and two other soldiers and two policemen were wounded, the Information Ministry official told SANA.
Security forces also detained a Jordanian named Sharif Ayad Saeed al-Smady, and the wife of his brother who was identified as Muhammad Islam. No further details were provided on the woman.
It was also unclear how many suspected rebels were involved in the battle. The official said the operation was mounted after several days of surveillance of the suspected group, which included those wanted for terrorist-related crimes and armed robbery.
Security forces are continuing operations against the group, the official said without elaborating.
The latest violence followed Sunday's clashes that killed what Syria described as an Arab extremist, plus two Syrian soldiers, near the Lebanese border.
On Sunday, Syria's Information Ministry said on its website that the US pressure was aimed at forcing Syria to change its position supporting resistance of occupation - a reference to the Hizb Allah group in Lebanon, which Washington considers a terrorist organisation.