REUTERS - Turkish President Tayyip Erdogan has written to Russian leader Vladimir Putin to apologize over the shooting down of a Russian air force jet by Turkey's military.

After the Russian jet was shot down in November last year near the Syrian-Turkish border, Russia imposed trade restrictions on Ankara. Putin had said they would not be lifted unless Erdogan apologized over the incident.

There was no immediate comment from Ankara.

In a statement, the Kremlin said Putin had received a letter from Erdogan "in which the Turkish leader expressed his desire to resolve the situation connected to the downing of a Russian military aircraft."

"The letter states, in particular, that Russia is a friend to Turkey and a strategic partner, with which the Turkish authorities would not wish to spoil relations," the Kremlin statement said.

It cited Erdogan as saying in the letter: "I want to once again express my sympathy and deep condolences to the family of the Russian pilot who died and I say: 'I'm sorry.'"

Turkey later confirmed the Kremlin's statement.

"The president also called on his Russian counterpart to restore the traditional friendly relations between Turkey and Russia, work together to address regional crises and jointly combat terrorism," Erdogan spokesman Ibrahim Kalin said in a statement.

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

The man suspected of killing the Russian air force pilot after his plane was shot down is being prosecuted, a Turkish official said.

Alparslan Celik, who was fighting with a Turkish-backed Turkmen brigade opposing government forces in northern Syria at the time, was detained at the end of March in the Aegean coastal city of Izmir on unrelated charges, but a court decided in May there was insufficient evidence against him.

Celik's prosecution was long demanded by Moscow.

The Turkish lira firmed to 2.9330 against the U.S. dollar from 2.9430 beforehand after the Kremlin said Erdogan had expressed his regret.