It also reported on Sunday the arrest of an unspecified number of armed men, captured after the exchange of fire, adding that 34 suspects were detained in a subsequent raid.
"The clash erupted when the extremist in question attempted to infiltrate Syria illegally from Lebanon along with other members of the extremist group," the report said.
"The extremist opened fire on the patrol leaving two dead. The extremist was killed and other members of his group captured. Security forces later detained 34 non-Syrian extremists in a raid on a flat where they found passports and identity cards."
According to Aljazeera's correspondent in Damascus, the dead assailant has been identified as Majdi bin Muhammad bin Saeed al-Zuraibi.
Al-Zuraibi is a Tunisian and was born in 1979, the correspondent said.
Sana, however, gave no details of the nationalities of the "extremists" or the group to which they were suspected of belonging.
Aljazeera reported that the clashes took place on Saturday near the northwestern city of Homs and that the group in question may be the Jund al-Sham (Soldiers of the Levant).
Last month, Damascus had announced that they had dismantled Jund al-Sham, which they said was plotting attacks against the capital's main law courts.
The group first emerged in late March when it claimed responsibility for a car bombing that destroyed a British-run theatre in the Gulf emirate of Qatar in which one UK national was killed.