The letter was the most significant in a series of signals from Ankara in recent weeks that it is keen to repair ties that plunged to historic lows after Turkey shot down the Russian war plane on November 24.

"We confirm media reports the president sent a letter to Russian President Vladimir Putin on the occasion of the Russian national day," the official said, referring to the Day of Russia marked on June 12.

"I hope our relations will reach a level they deserve," Erdogan told Putin in the letter, according to the private NTV television channel.

The full contents of the letter were not made public.

- Ex-friends at odds -

In Moscow, Kremlin spokesman Dmitry Peskov confirmed that Erdogan had sent Putin the message, saying it was received "via diplomatic channels", the Ria-Novosti news agency reported.

Turkey''s downing of the Russian jet on its border with Syria in November sparked an unprecedented crisis in the two nations'' relationship, which was then exacerbated by Moscow''s role in the Syrian war.

Turkey says the Russian plane strayed into its airspace and ignored repeated warnings, but Russia insisted it did not cross the border and accused Ankara of a "planned provocation."

Erdogan wanted to meet with Putin for face-to-face talks on the sidelines of a climate summit in Paris after the plane crisis, which was rebuffed by the Russian leader.

Prime Minister Binali Yildirim also sent a letter to his Russian counterpart Dmitry Medvedev on the occasion of the Russian national day, the Turkish official said.

Turkey did not participate at the ministerial level in the national day reception at the Russian embassy in Ankara last Friday.

In recent months, Turkish authorities have struck a reconciliatory tone to restore ties, with Erdogan hoping to get back to previous robust relations with Moscow.

Before the the plane crisis erupted, Turkey and Russia had strong cooperation on many issues, putting disagreements on Syria and Russia''s annexation of Crimea from Ukraine to one side.

- ''Back to old days'' -

Turkey is largely dependent on Russian gas and oil for its energy supplies and before the crisis the two sides had been targeting $100 billion (89 billion euros) in bilateral trade volume by 2023.

Erdogan has admitted that ties with Moscow reached a "rupture point" over the plane crisis but expressed hope they would regain their former strength.

"With Putin, we brought bilateral ties to a very advanced level. Our trade volume with Russia was much more than that with America ... It is saddening to see such strong ties reach the current state," he said in comments published in the Hurriyet newspaper Saturday.

"I hope our relations will recover in a short time and we''ll get back to our old days again with new vigour."

Turkish Foreign Minister Mevlut Cavusoglu has also suggested to form a joint working committee between the two countries to address problems.

However, Turkey has so far shown no sign of meeting Russia''s key conditions of an apology and bringing to justice those responsible for the death of a Russian pilot of the downed plane.

The Turkish official said the letter should be seen as "a token of Turkey''s goodwill" and expressed hope Moscow would also act "in a responsible and constructive manner".

The crisis in relations severely hit Turkey''s tourism industry, with the number of Russian tourists drastically declining in southern holiday resorts along the Mediterranean coast.