Moscow is lifting travel restrictions on Russian tourists visiting Turkey after a period of diplomatic tension with plans to resume "mutually advantageous" trade relations.

Russia's President Vladimir Putin said on Wednesday that he asked his government to begin "the process of normalising general trade and economic ties with Turkey", fixing badly strained relations since Ankara shot down a Russian warplane taking part in Moscow's military campaign in Syria last year.

"I want to start with the question of tourism ... we are lifting the administrative restrictions in this area," Putin told government ministers in televised comments.

Russian tourism to Turkey last month was down more than 90 percent year on year, according to figures by Turkey's Ministry of Culture and Tourism.

Overall tourism in Turkey was down about 35 percent last month compared with the same period last year, the ministry said.

'Sorry'

The development came days after Turkish President Recep Tayyip Erdogan expressed regret for the downing of the Russian jet in a letter this week to Putin.

The Russian leader said the letter created conditions to close "this crisis chapter" in bilateral relations.

On Wednesday, Putin and Erdogan held a "constructive" telephone conversation, according to the Kremlin.

Putin 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.

READ MORE: Erdogan 'sorry' for downing of Russian jet

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

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. But Putin's spokesman Dmitry Peskov told the Russian Interfax news agency that the meeting's time and place have yet to be arranged.

They also 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.