Putin made the remark during a meeting with Russian diplomats in Moscow on Thursday.
The remarks come as officials in Ankara say they had expressed regret only not an apology over the incident.
Moscow-Ankara relations became strained last November after Turkey shot down a Russian Sukhoi Su-24 aircraft with two pilots aboard, claiming the fighter jet had repeatedly violated Turkish airspace.
Ankara argued that the Russian plane strayed into its airspace and ignored repeated warnings. Russia, however, insisted the aircraft did not cross the border and accused Ankara of "planned provocation."
Moscow said the plane was brought down in Syrian airspace, where Russia has been conducting combat sorties against Takfiri terrorists since late September 2015 upon a request from the Damascus government.
Of the two pilots aboard the warplane, one was rescued with the help of the Syrian army, but the other was killed by militants fighting the Syrian government.
On Monday, the Kremlin said Putin had received a letter from Turkish President Recep Tayyip Erdogan, in which he had apologized to his Russian counterpart over Ankara’s shooting down of the Russian jet.
Turkey, however, said later it had only expressed regret to Russia, denying reports of an apology, and retracting a compensation pledge.
A combo taken from video shows a Sukhoi Su-24 fighter jet crashing in a mountainous area in northern Syria after it was shot down by Turkish fighter jets near the Syrian border on November 24, 2015. ©Reuters
Two days later, Putin ordered his government to start the process of normalizing trade ties with Turkey, following a telephone conversation between the Russian and Turkish leaders, during which Putin expressed sympathy for the victims of the Tuesday night gun and bomb attacks at Istanbul's Ataturk international airport, which claimed the lives of 42 people and injured more than 230 others.
"I ask that the Russian government begins the process of normalizing general trade and economic ties with Turkey," Putin said at a cabinet meeting on Wednesday, following the telephone conversation.
Following the November 2015 incident, Russia imposed a raft of sanctions against Ankara, including economic bans, and suspended all military deals with Ankara.
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