Six jets were sent to the area in response to three such incidents on Saturday, the statement said, adding that there was no violation of Turkish airspace.
Last month, Syrian forces shot down a Turkish jet in the border area.
The incident further strained already tense relations between former allies.
Turkey's government has been outspoken in its condemnation of Syria's response to the 16-month anti-government uprising, which has seen more than 30,000 Syrian refugees enter Turkey.
On Friday, Turkey said it had begun deploying rocket launchers and anti-aircraft guns along the border in response to the downing of its F-4 Phantom jet on 22 June.
The move came after Prime Minister Recep Tayyip Erdogan warned that Turkey had changed its rules of military engagement and would now treat any Syrian military approaching the border as a threat.
Syria said the Turkish F-4 was shot down by air defence fire inside its airspace. Turkey insists it was downed by a missile after briefly entering and the leaving Syrian airspace.
The plane crashed in the Mediterranean, off the coast of the southern province of Hatay. Its pilots are still missing.
Mr Erdogan spoke of Turkey's "rage" at the incident and described Syria as a "clear and present threat".
Nato condemned the attack and voiced strong support for Turkey, after Ankara invoked Article 4 of Nato's founding treaty, which entitles any member state to ask for consultations if it believes its security is threatened.
Four of the six jets were scrambled on Saturday from the airbase of Incirlik in response to two occasions of Syrian helicopters flying close to Hatay province, Sunday's army statement said.
Later, two more F-16s took off from a base near Batman, in southeastern Turkey, after Syrian helicopters were spotted close to the province of Mardin, it added.
The military said the helicopters flew as close as 6.5km (4 miles) to the border, according to the AP news agency.
Regional impact
The border incident comes after the UN and Arab League envoy on Syria, Kofi Annan, warned of the danger of the Syria conflict spilling over into the wider region if the bloodshed is not stopped.
He was addressing an international meeting of major international and regional powers in Geneva on Saturday, aimed at reviving the six-point peace plan for Syria brokered by Mr Annan.
The countries present at the Geneva talks reached an agreement calling for a ceasefire and a transitional government in Syria.
Western demands to exclude President Bashar al-Assad and his allies from the interim administration reportedly foundered on opposition from Russia.
Moscow sees Syria as its closest ally in the region, and rejects any attempt to impose a solution on Syria from the outside.
The Paris-based opposition Syrian National Council rejected the Geneva deal as too ambiguous, according to the AP news agency.
Violence has worsened in Syria recently despite the cease-fire mediated by Mr Annan as part of his six-point plan earlier this year.
On Friday, government forces recaptured the Damascus suburb of Douma - an opposition stronghold - after 10 days of artillery bombardment. Activists described conditions in the town as "catastrophic".
Activists estimate that as many as 15,800 have died since the uprising began early last year. Casualties figures are difficult to verify, as Syria does not allow foreign journalists to operate on its territory.
The conflict is seen as becoming increasingly militarised, with both rebels and government forces thought to be receiving arms supplies from abroad.
Source:http://www.bbc.co.uk/news/world-europe-18666165
