Bulgaria agreed to stop allowing Russian aircraft flying to Syria into its airspace, a former CIA official has told CBS News.

In the words of former CIA Deputy Director Michael Morell, the US can respond to Russia's actions of strengthening its military presence in Syria by cutting off air routes it is using for shipments.

"One is to overfly Turkey. The Turks have said no. There's been a long history to that. The other way, and that's what's been happening, is over Bulgaria and Greece. But now the United States has reached out and the Bulgarians have agreed no more flights."

Morell's comments follow a decision by Bulgaria to ban a Russian convoy purportedly delivering humanitarian aid to Syria from overflying on Tuesday.

That prompted Moscow MPs to allege Bulgaria was acting upon US instruction.

A day earlier, Bulgaria granted passage to a Syria-bound Russian passenger jet with diplomats on board.