The Syrian army has taken control of the northern town of Jisr al-Shughour following what state media has described as heavy fighting.
A BBC reporter embedded with troops says clashes erupted after the army entered the town at dawn. Sources said three people had died.
The government said it was trying to restore order after 120 security personnel were killed last week.
Residents say they died after a mutiny and fighting between security forces.
The government operation sent hundreds more people fleeing towards the Turkish border, to join thousands who have already crossed.
BBC correspondents on the border say the number of those who have crossed is probably higher than the official figure of 5,050 given on Sunday afternoon by the UN’s refugee agency, the UNHCR.
Witnesses said there might be as many as 10,000 sheltering in the area.
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.
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The official version is improbable. Most people had left Jisr al-Shughour after seeing the regime’s scorched earth policy”
Western diplomat in Damascus
“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.”
Human rights activists and residents said troops began bombarding Jisr al-Shughour early on Sunday. They then began to move in from the east and south in a two-pronged attack with 200 military vehicles, they added.
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At the scene
BBC Arabic reporter, embedded with Syrian troops at Jisr al-Shughour
The army has just completed a wide-ranging operation that started early in the morning in the town. Tanks and armoured vehicles have taken up positions inside the town while its residents have remained indoors.
A military spokesman said many had fled the town in three directions – to the surrounding mountains, to the Turkish border, and to a nearby town, Maarat al-Numan, which they now control.
During the operation, the source says, a number of people were arrested. Syrian troops have not taken positions along the Turkish border but have established checkpoints nearby.
Many wheatfields appear to have been burned. The source says intermittent clashes have continued between the army and gunmen. Seven bodies, believed to be those of security forces, have been recovered from a grave in the area, he adds.
Helicopter gunships were also seen hovering overhead.
The BBC Arabic correspondent accompanying the troops confirmed that there had been clashes after the advance began at dawn.
An Associated Press reporter meanwhile said he had seen two bodies at the National Hospital, which he said was damaged, with a burned-out ambulance outside.
State TV said there had been “heavy confrontations” between “army units and members of armed organisations taking up positions in the surroundings of Jisr al-Shughour and inside it”.