The Kremlin reported Monday Turkish President Recep Tayyip Erdogan sent a message to Russian President Vladimir Putin saying "I am sorry" for the downing of a Russian jet last November, an incident Putin had called a "treacherous stab in the back."

Erdogan expressed his "sympathy and deep condolences" to the family of the killed pilot and "asked to be forgiven," Putin's spokesman Dmitry Peskov told reporters.

The letter added that Turkish authorities were conducting a probe against a Turkish citizen who allegedly shot and killed the plane's pilot as he was descending by parachute, the Kremlin added. The plane's co-pilot survived and was rescued, but a Russian marine was killed by militants during the rescue mission near the border.

Erdogan spokesman, Ibrahim Kalin, said, according to Turkey's state-run Anadolu news agency, that the Turkish leader expressed his deep regret: "In the letter, the president stated that he would like to inform the family of the deceased Russian pilot that I share their pain and to offer my condolences to them. May they excuse us."

Turkey had previously claimed two of its F-16s shot down the Russian Su-24 bomber because it violated Turkish airspace near the Syrian border and failed to heed warnings to turn around. The co-pilot told Russian media he never received such warnings.

The Russians responded by halting package tours to Turkey, banning most agricultural imports from Turkey and introducing other measures restricting bilateral trade. Before the plane's downing, Russia had been the largest destination for Turkish exports, mostly textile and food, and also the biggest source of Turkish imports.

The downing of the plane reflected simmering tensions between Russia and Turkey, which had backed opposing sides in the Syrian conflict. Russia's air campaign, which began in September, helped shore up Syrian President Bashar Assad, whose foes have been backed by Turkey.

Lifting the crippling restrictions was essential for Erdogan, who has found himself under pressure both at home and abroad. Since the incident, Erdogan and his ministers have continuously spoken in favor of normalizing ties with Moscow, but Putin made it clear that he expected a formal apology and a compensation of damage.

Erdogan's office also said that the Turkish leader called on Putin to restore the traditional friendly relations between Turkey and Russia and work together to address regional crises and jointly combat terrorism

"We are pleased to announce that Turkey and Russia have agreed to take necessary steps without delay to improve bilateral relations," Erdogan spokesman Kalin said.

The Associated Press contributed to this report.