Iran's rial currency sank to a record low against the U.S. dollar on Saturday despite central bank measures aimed at cooling demand for foreign currency from savers worried about inflation and the country's economic prospects.

The rial was trading at 575,000 on the unofficial free market against the dollar, compared to 540,000 on Friday, according to foreign exchange site The website also gave the rate as 575,000.

With annual inflation running at more than 50%, Iranians have been trying to protect the value of their savings by buying foreign currency or gold.

Seeking to cool the market and ease demand for dollars, the central bank on Saturday lifted a ban on private exchange shops selling hard currencies.

Last week, it opened an exchange centre to allow ordinary Iranians to purchase foreign currency, but some market analysts said the move had yet to dampen appetite for greenbacks.

"While some analysts expected that, with the opening of this centre, emotional trading on the free market would decrease, the dollar continued its upward movement ... and the fervour has become even more intense on the futures market," economic website Ecoiran said.

The rial has lost nearly 45% of its value since nationwide protests following the death in police custody of a young Kurdish Iranian woman began in September.

The unrest has posed one of the biggest challenges to theocratic rule in Iran since the 1979 Islamic revolution.

Foreign exchange traders say the rial's depreciation stems partly from the unrest and Iran's increased isolation in the face of Western sanctions over its human rights record and Russia's use of Iranian-made drones in Ukraine.

The reimposition of U.S. sanctions in 2018 by then President Donald Trump have harmed Iran's economy by limiting Tehran's oil exports and access to foreign currency.

Since September, nuclear talks between Iran and world powers to curb Tehran's nuclear programme in exchange for the lifting of sanctions have stalled, worsening economic expectations for Iran's future.

(Reporting by Dubai newsroom, Editing by Helen Popper)