Syrian Foreign Ministry spokesman Jihad Makdissi said the plane was shot down in Syrian airspace, disputing Turkey's claim that it was downed over international waters after briefly straying into Syrian airspace by mistake.
"What happened was a violation of Syrian airspace. Even Turkey says Syrian sovereignty was violated. Regardless of whether it was a training mission, a reconnaissance mission, it was a violation," Makdissi said.
He insisted that Syria was the wronged party, not Turkey.
Also Monday, a spokesman for the Turkish Foreign Ministry told CNN that Syria fired Friday on a second Turkish plane that was part of a search-and-rescue mission sent in after the jet was shot down. The plane, which entered Syrian airspace in search of the jet, was not hit, said Selcuk Unal.
"There was no injury, nobody was harmed. But that plane immediately returned to Turkish airspace. And through military diplomatic channels we informed them: 'What's going on?' " Unal said.
The Turkish Foreign Ministry said Sunday that it considered the shooting to be a hostile act. Turkey delivered the message in a diplomatic note to the Syrian consulate in Istanbul, Unal told CNN.
In addition to NATO, Turkey also submitted a letter about the incident to the U.N. Security Council. The country made no request for action, but outlined its version of events.
"This attack at the international airspace, causing possible loss of two Turkish pilots, is a hostile act by the Syrian authorities against Turkey's national security. Thus, we strongly condemn it," read the letter, dated Sunday.
It identified the downed plane as a Turkish RF-4 reconnaissance aircraft, a version of the McDonnell Douglas F-4 Phantom II. It was flying alone, without arms, in international airspace when it was shot down, the letter read.
Turkish search-and-rescue teams found the wreckage of the jet in the Mediterranean Sea on Sunday, about 1,300 meters (4,260 feet) underwater, Foreign Ministry spokesman Unal said.
Tension between Syria and Turkey escalated sharply in the 1990s over Kurdish militancy.
Turkey was angry that the Syrian regime harbored Kurdish militant Abdullah Ocalan.
Ocalan founded the Kurdistan Workers' Party, the PKK. The group, regarded as a terrorist organization by Turkey and the United States, has been fighting the Turkish government for Kurdish autonomy.
Syria eventually expelled Ocalan and the hostility eased. Syrian-Turkish political and economic ties grew after Erdogan became prime minister in 2003. But over the last year, Erdogan's government grew disgusted with the al-Assad regime over the government's brutal crackdown against Syrian citizens during the uprising.
Some observers believe Syria is now supporting the PKK.