In an interview with Turkey’s Cumhuriyet newspaper, Bashar al-Assad argues that the plane was flying in an area previously used by Israel’s air force.
The plane went down in the Mediterranean last month and the two pilots have not been found.
The incident has heightened tensions between the two countries.
Last week, Turkish PM Recep Tayyip Erdogan condemned Syria’s action and described the neighboring country as a “clear and present threat”.
Turkey reinforced border areas with rocket-launchers and anti-aircraft guns.
On Sunday, Turkey said it had scrambled six F-16 fighter jets when Syrian helicopters had approached the border.
“We will not allow (the shooting down) to turn into open combat between the two countries,” President Bashar al-Assad is quoted as saying.
Cumhuriyet, which published the interview on Tuesday, does not indicate when it took place but shows a picture of Bashar al-Assad standing beside its Ankara bureau chief Utku Cakirozer.
In other developments:
• Turkish media reported late on Monday that another 85 Syrian soldiers, including 14 senior officers, had defected across the Turkish border. It is one of the biggest groups of army defections since the March 2011 uprising in Syria began.
• Syria has been accused of practicing a widespread policy of state-sanctioned torture, in a Human Rights Watch report . The group says it has identified at least 27 detention centres across Syria.
• UN human rights chief Navi Pillay has said that both Syrian government forces and the opposition have been involved in operations that harmed civilians. She has appealed for further militarization of the conflict to be avoided at all costs.
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