One of the most widely contested religious buildings in Turkey, Hagia Sophia, should be returned to the Orthodox Church, Russian officials have said.

"The Russian side... expect[s] from the Turkish side a friendly step – to return the Cathedral to the hands of the Orthodox church of Constantinople," Russian MP Sergei Gavrilov told Russia's RCB TV.

"The Russian side is ready to provide financial assistance and enlist the best Russian restorers and scientists' aid in the restoration of the ecumenical Christian artefact. Such a step would help Turkey and Islam to show that good will is above politics."

An ancient Byzantine church, Hagia Sophia is located in Istanbul and renowned for its architecture. Once the world's largest cathedral, it was turned into a mosque in the 1400s and later closed in 1931.

The secular Turkish government opened it as a museum in 1935, but there have been calls for it to be turned back into a mosque by the increasingly Islamist government of Recep Tayyip Erdogan.

Tensions have escalated between Turkey and Russia since Turkey downed a Russian warplane in its airspace last week.

The first known incident of its kind since the Cold War, Turkey shot down the Russian bomber on 24 November and relations between the two countries have rapidly deteriorated.

Turkey's prime minister today refused to apologise for the incident.

"No country should ask us to apologise," Ahmet Davutoglu told reporters. "The protection of our land boarders, our airspace, is not only a right, it is a duty. We apologise for committing mistakes, not for doing our duty."

Gavrilov admitted that relations between Turkey and Russia were undergoing an "endurance trial", but said that made the return of the Hagia Sophia to the Church especially important.