The gunbattle on Mount Qassioun overlooking the Syrian capital was the second fire-fight with extremists in recent days and comes amid intense US pressure on Syria to stop militants slipping over its border into Iraq.
“The clash took place early on Monday on Mount Qassioun with a group of people wanted for terrorist crimes, some of whom were former bodyguards of Saddam Hussein,” the SANA agency said.
“Two terrorists were arrested after the clash,” which also claimed the life of a security forces officer.
Quoting an information ministry official, SANA said the two people arrested were a Jordanian named Sharif Aied Saif Smadi and the wife of his brother Mohammed.
The Smadi brothers are wanted in Jordan for a series of petty crimes including armed robbery.
The new clash came a day after SANA reported two Syrian security personnel and an “Arab extremist” were killed in a firefight while trying to cross the border from Lebanon, during which several militants were captured.
The authorities also announced last month they had dismantled an “Islamic fundamentalist group” which they said had been plotting attacks against targets in Damascus.
The latest clash comes as US stepped up pressure on Syria to seal its borders to insurgents.
US Defence Secretary Donald Rumsfeld said last week the Syrian government must know that foreign fighters are being funnelled through its territory into Iraq and “at a minimum are tolerating it.”
The US has also frozen the assets of Syria’s Interior Minister Ghazi Kanaan and top military intelligence chief Rustum Ghazali, accusing them of abetting terrorism.