MOSCOW/ANKARA (Reuters) - The presidents of Russia and Turkey agreed on Wednesday to resume bilateral cooperation, including in the fight against terrorism, after a period of diplomatic tension and said they wanted to hold a face-to-face meeting.

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Relations between Moscow and Ankara have been badly strained since Turkey last year shot down a Russian warplane taking part in Moscow’s military campaign in Syria.

Turkish President Tayyip Erdogan expressed regret for the incident this week in a letter to President Vladimir Putin. The Kremlin leader said the letter created conditions to close “this crisis chapter” in bilateral relations.

Both Moscow and Ankara said the two presidents had held a “constructive” telephone conversation on Wednesday.

Putin said he would order the government to start talks with Turkey on resuming “mutually advantageous” trade relations and to drop restrictive measures on Russian tourists visiting Turkey, the Kremlin said in a statement.

“The conversation was in general businesslike and constructive, aiming to restore the traditionally friendly mood of the multi-faceted bilateral cooperation,” the Kremlin said.

Turkish presidential sources called the conversation “very productive and positive”. They said Putin and Erdogan were expected to meet before and during a G20 summit in September in China.

Putin also expressed his condolences to Erdogan after three suspected Islamic State suicide bombers opened fire and blew themselves up in Istanbul’s main airport late on Tuesday, killing at least 41 people and wounding some 239.

Putin and Erdogan both stressed the need for closer cooperation in tackling terrorist threats, the Kremlin said.

The Russian leader told Erdogan he hoped that a criminal case launched against a Turkish citizen accused of killing the Russian pilot of the downed warplane would be an objective one.

Ankara has said it acted lawfully in shooting down the plane, saying it had crossed from Syria into Turkish air space; Moscow denied that happened.

Putin and Erdogan agreed that their foreign ministers would meet on the sidelines of a regional summit in Russia’s Black Sea resort of Sochi this week to discuss the situation in Syria and further development of bilateral ties.

In Syria, Russia backs President Bashar al-Assad while Turkey, with its Western allies, supports rebel forces seeking to unseat the Syrian leader.