Hundreds have fled in the last 24 hours, the agency said, citing local sources.
Most came from Jisr al-Shugur, a city in northwestern Syria roughly 40 kilometres (25 miles) from the Turkish border that is the latest flashpoint in the anti-regime uprising to come under assault by Syrian security forces.
On Friday, Syrian television said the army was forced to intervene because "armed groups" had allegedly committed atrocities in the city.
Dozens more Syrians were waiting in no man`s land to enter Turkey, the all-news television station NTV reported.
After crossing the border, the refugees are escorted by Turkish police either to area hospitals or to one of three makeshift tent villages in Yayladagi, in Turkey`s Hatay province.
Some 60 people have been hospitalised so far, the news agency said.
The authorities have set up a field hospital in Yagladadi to provide emergency care, with about 40 beds in four tents. A mobile laboratory with equipment including X-ray machines is on its way, Anatolia reported.
The Turkish Red Crescent has started building more camps to the northeast of Yayladagi, in Altinozu and Boynuyogun, capable of holding 4,000 and 5,000 people respectively, in anticipation of more refugees to come as the conflict in Syria continues.
Turkish foreign ministry official Halit Cevik declined to estimate the number of Syrian refugees that may cross the border in the coming days.
"Turkey has made every effort to welcome the Syrian refugees," Cevik told journalists after touring the camps.
Turkey`s Prime Minister Recep Tayyip Erdogan, a personal friend of Syrian President Bashar al-Assad, said Friday that Syrian troops "do not behave humanely."
He called the crackdown in Jisr al-Shugur "unacceptable," and slammed the treatment of the bodies of women slain by Syrian security forces as an "atrocity", Anatolia reported. (*)