Ban said a "credible and thorough review" of the incident would help clarify what happened and prevent a repeat.
The Russia SU-24 attack plane was shot down earlier Tuesday by two Turkish F-16s after it violated Turkish airspace 10 times within a five-minute period, the Turkish army said.
Russia insisted that the fighter jet was inside Syrian territory and President Vladimir Putin warned of "serious consequences" for Russian-Turkish relations.
"The secretary-general urges all relevant parties to take urgent measures with a view to de-escalate the tensions," said UN spokesman Stephane Dujarric.
"Our rules of engagement are well known and are reiterated to all parties on numerous occasions," wrote Cevik.
"Turkey will not hesitate to exercise its rights emanating from international law to protect the security of its citizens and borders."
Russian warplanes have been pounding Syrian rebels and Islamic State fighters, backing government forces at the request of Syrian President Bashar al-Assad.
Turkey has sided with the US-led coalition that launched air strikes last year to defeat the Islamic State group.
British Ambassador Matthew Rycroft, whose country chairs the council this month, said a meeting could be held if requested and that the incident was not raised during a morning session.
Rycroft said he was "extremely concerned" and stressed the importance of "deconfliction" measures to prevent clashes in the air campaigns being waged by Russia and the US-led coalition in Syria.
In his letter to the council, the Turkish ambassador repeated the army's assertion that the Russian plane had been warned 10 times in five minutes via an emergency channel to change its headings south immediately.
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