Hundreds of Syrians have been massing on the northern border with Turkey, preparing to cross over if the army advances further into the area after seizing the town of Jisr al-Shughour.
Syrian military sources have told the BBC the army plans to move on the nearby town of Maarat al-Numan.
It says it is pursuing armed men who escaped the weekend offensive. State media said there was heavy fighting.
Turkey has already taken in thousands of refugees from northern Syria.
The government said it was trying to restore order after 120 security personnel were killed in Jisr al-Shughour last week.
Residents say they died after a mutiny and fighting between security forces.
Syria has prevented most foreign journalists from entering the country, making it difficult to independently verify reports from there.
Continue reading the main story Watching and waiting.
The BBC's Owen Bennett-Jones, who is on the Turkish side of the border with Syria, says more than 5,000 refugees have registered with officials.
However, another 5,000 have entered the country unofficially, he says, while hundreds more are massed at the border, waiting for the army's next move.
Many of them are reluctant to abandon their vehicles or livestock, our correspondent says, and will only cross if the army advances into the area. Others are waiting for relatives.
Human rights activists and residents said troops began bombarding Jisr al-Shughour early on Sunday.
Helicopter gunships were also seen hovering overhead.
But speaking to the BBC, an army general denied any shelling. The troops were only after those responsible for the killings of security personnel earlier this week, the general insisted.
The army has now taken control of the area.
A BBC Arabic correspondent embedded with the Syrian military says tanks and armoured vehicles have taken up positions inside the town. Buildings still bear the marks of clashes, and wheat fields have been burned.
Still from Syrian TV of what it described as mass grave (credit: AFP/HO/Syrian TV) Syrian TV showed images of what it described as a mass grave in Jisr al-Shughour
However, state media report that only two "armed members of terrorist gangs" were killed in the offensive, while the army says one soldier was killed and four wounded.
A military spokesman told our Arabic correspondent that armed men from Jisr al-Shughour who fled to Maarat al-Numan would be dealt with in a military operation in the next few days.
Separately, the bodies of 10 security personnel were recovered from a mass grave. Correspondents who witnessed the exhumation said four had been beheaded, and most of the bodies were riddled with bullet wounds.
There are continuing but unverifiable reports of army defections, with the latest saying an officer and 50 men had changed sides rather than fire on civilians in Jisr al-Shughour.
'Forced to flee'
US officials say the crackdown has created a humanitarian crisis, and called for the International Committee of the Red Cross (ICRC) to be given access to Syria.
"No-one is aware of the real magnitude of the problem and this is a big issue, because it does not allow us to know the size of the problem and then to act accordingly," ICRC spokesman Hicham Hassan told the BBC.
On the Turkish side, two camps are already full of refugees and a third is filling up rapidly.
"The situation is grim. People were forced to flee with a few possessions. We are relying on the Turkish authorities for everything," Mohammed, one of those in the border area, told the BBC.
"No-one knows when it will be safe to return to our homes. When we return, people expect to find their homes destroyed and bodies unburied."
Protests against President Assad, who succeeded his father Hafez in 2000, began in mid-March and have spread across the country.
Human rights groups say more than 1,200 people have been killed in the crackdown.
