Turkish President Recep Tayyip Erdogan apologized Monday for the downing of a Russian warplane in November and called for Russia and Turkey to mend a bilateral relationship that has become openly hostile over the incident.

One Russian pilot was killed last year when two Turkish F-16s shot down a Russian Su-24 warplane over Turkey’s border with Syria in an unexpected clash that Russian President Vladi­mir Putin called a “stab in the back administered by the accomplices of terrorists.” In footage later aired on Russian state television, pro-Turkish rebels fired automatic rifles at the pilot as he parachuted to the ground. The Kremlin was furious, imposing a series of punishing sanctions against Ankara while demanding for months that Erdogan personally apologize.

On Monday, Erdogan wrote to Putin 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.” In a statement, Erdogan’s press secretary said Russia and Turkey “have agreed to take necessary steps without delay to improve bilateral relations,” specifically noting regional crises and the fight against terrorism.

“We had no wish or intention to down a plane of the Russian Federation,” a Kremlin press release quoted the Turkish communique as saying. “I share their pain with my whole heart,” Erdogan wrote, referring to the family of the pilot.

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The personal apology from one of the region’s most autocratic politicians came on a day of diplomacy that dealt with some of the international tension he has generated in recent years. Turkey on Monday also normalized relations with Israel, ending a six-year rift over the killing by Israeli commandos of Turkish activists aboard an aid ship bound for the Gaza Strip.

Soner Cagaptay, director of the Turkish Research Program at the Washington Institute for Near East Policy, said Russia had ratcheted up pressure on Turkey over the incident.

“Russia has been very aggressive against Turkey, militarily and in intelligence and cyber realms since the 2015 November plane incident,” he said. “This scares Erdogan tremendously. If the joke in Turkey was that Erdogan, the sultan, would never apologize, the answer would be ‘yes, but except to the tsar.’ ”

The Turkish attack on the Russian jet occurred not quite two months after Moscow intervened militarily in Syria to back the regime of President Bashar al-Assad and carry out airstrikes against a broad swath of the secular and Islamist opposition. A rescue operation to save the pilot also ended in disaster, as a Russian marine was killed after rebels downed a rescue helicopter.

At the time, Turkey claimed that the Russian pilot had flown into its territory and bombed rebel positions occupied by Turkmen rebels, whom Erdogan had backed and armed against the Assad government. It was not immediately clear whether Turkey was renouncing those claims Monday.

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Russia, which had maintained friendly relations with Erdogan and saw the country as a potential counterweight to Europe, reacted angrily to the incident. It intensified attacks on Turkish-backed rebels in northern Syria and imposed a series of painful sanctions on Turkish imports and labor, as well as on Russian tourism to Turkey, that have cost that country billions.

The Kremlin has insisted for months on a personal apology as well as the prosecution of the alleged killer of the pilot. In another concession Monday, a regional Turkish prosecutor announced that he would prosecute Alparslan Celik, a Turkish national fighting alongside Syrian rebels, for the death of the Russian pilot.

While Turkey and Russia may resume normal relations, they remain on opposing sides of the Syrian crisis, with Moscow backing Assad’s government and Erdogan calling for him to step down.

Russia said Monday that Putin had received the apology, but no reaction was reported.

Cunningham reported from Istanbul.

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