Istanbul (CNN) -- Turkey scrambled fighter jets three separate times Saturday as Syrian helicopters neared the border between the two countries, Turkey's military said Sunday.
The helicopters were in Syrian airspace, but were getting close to the border, the armed forces statement said.
The jets -- a total of six -- were scrambled twice out of Incirlik, and once out of Batman, it said.
The incident underscores rising tensions between the two nations in the wake of Syria's downing a Turkish F-4 Phantom jet on June 22.
Both Syria and Turkey acknowledged the plane strayed into Syrian airspace, but Turkey said the incursion was accidental and quickly corrected.
Turkey's National Security Council said last week the nation would act against "hostile action" by Syria. Turkey also bolstered its forces along the border.
Also, Turkish Prime Minister Recept Tayyip Erdogan said his country was changing its military rules of engagement and would treat a military approach toward its borders by Syria as a potential threat that "will be dealt with accordingly."
The downing of the jet drew sharp condemnation from NATO, but the alliance did not promise any action in response to the incident. Turkey did not invoke the NATO article calling for collective defense of members, NATO Secretary General Anders Fogh has said.
A senior U.S. official said Turkey asked NATO members to study a range of ways a no-fly zone could potentially help the situation and ease threats. It was "not clear what, if anything, will be done," the official said last week.
A search for the pilots of the downed jet was ongoing. The wreckage of the plane has also not been located.
A man from the border village of Guvecci, who asked not to be named for security reasons, said Thursday military personnel and equipment had been arriving for the past two or three days. Turkish state television also reported air-defense systems and tanks were among the equipment.
CNN's Ivan Watson and Elise Labott contributed to this report.