The interior ministry issued the warning as thousands of protesters dug in at a main square in the central city of Homs, vowing to stay put until their demands are met.
"The latest incidents have shown that... armed Salafist groups, particularly in the cities of Homs and Banias, have openly called for armed revolt," said a ministry statement carried by the official SANA news agency.
It accused such groups of killing soldiers, policemen and civilians, and of attacking public and private property, and warned that "their terrorist activities will not be tolerated".
The authorities "will act with determination to impose security and stability in the country" and will "pursue the terrorists wherever they are in order to bring them to justice and end the armed revolt", it said.
The ministry called on people to "name the places where the terrorists and suspects are and not to allow them to live among them".
Activists reported that more than 20,000 demonstrators erected tents in the main square of Homs a day after 11 people were killed by security forces in the city and a nearby town during a day of massive nationwide protest.
Syria has been rocked by deadly demonstrations since Saturday when President Bashar al-Assad vowed to lift nearly five decades of draconian emergency law -- a promise activists say is not enough.
"More than 20,000 people are taking part in the sit-in at Al-Saa Square (Clock Square) and we have renamed it Tahrir Square like the one in Cairo," rights activist Najati Tayyara told AFP from Homs.
The protesters put up tents in the square, copying demonstrators in Egypt who forced out veteran president Hosni Mubarak in February after 18 days of protests in Cairo's emblematic Tahrir Square.
"It is an open-ended sit-in which will continue until all our demands are satisfied," Tayyara said.
"This despotic regime must change. We have been waiting for 11 years for reforms," said Tayyara of the 11-year rule of Assad, who succeeded his autocratic father Hafez following his death in 2000.
Protesters in Al-Saa Square chanted "sit-in, sit-in until the fall of the regime," and "Freedom, Freedom".
The people are demanding greater freedoms, the release from jail of all political prisoners and an end to arbitrary arrests on political grounds, he said.
"The young people are ready to face anything, including martyrdom." Noora told AFP of the sit-in: "All of Homs is here."