Syrian and Russian news outlets reported the shootdown, saying the jet was hit by Syrian air defenses in southern Syria Thursday.
"We did not shoot down an Israeli plane", the official said, contradicting reports from Thursday night quoting a Syrian defense official that air defense systems had shot at and downed "hostile targets".
"At this point, it remains unclear if the launch indeed landed in Israeli territory", it said, adding that Israeli troops were searching the area for possible remnants of the missile.
Another missile hit the area of Harfa, near the Israeli border, where there is a Syrian military base, the UK-based monitor said.
"Furthermore, the report about a strike on an Israeli aircraft or an Israeli aerial target are bogus", said the statement.
Military sources told SANA that the incoming projectiles were heading toward the al-Kiswah area.
The Israeli Army says they recovered the wreckage of what is believed to be a Syrian surface-to-air missile in Golan, and are searching the area further.
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The strikes targeted the region of Al Kisweh, south of the Syrian capital, hitting Iranian militias' targets, according to Al-Hadath's sources.
For its part, the Israeli military denied any of its assets were hit, but stopped short of denying it had conducted strikes. It was not immediately clear who was behind the attack but Israel has carried out dozens of airstrikes on Syria over the past years.
Moscow pinned responsibility for the downing of its jet on Israel, saying its plane used the larger Russian one for cover, an allegation Israel disputed.
Syria complained to the United Nations about the incident, blaming Israel.
Israeli Prime Minister Benjamin Netanyahu told Moscow, however, that his government would continue to hit hostile targets in Syria and "continue security coordination" with Russian Federation.
Moscow blamed Israel for the incident and supplied Damascus with the advanced S-300 air defense system - something it had previously refrained from doing following requests from Jerusalem.