By Marat Gurt

ASHGABAT (Reuters) - Turkmenistan, which rights groups view as one of the most repressive countries in the world, celebrated President Kurbanguly Berdymukhamedov's 58th birthday on Monday by opening a park in the capital Ashgabat bearing his name.

It was the latest tribute to the leader who took over the Central Asian nation after the death of his predecessor in December 2006. Last month, Turkmenistan unveiled a gilded 6-metre-high statue of Berdymukhamedov on horseback perched on a white cliff.

A dentist with a passion for horses and fast cars, his rule has been marked by a rising personality cult.

Several thousand people chanted "Thank you Arkadag," the president's official title which means "The Patron" in Turkmen, as the ribbon was cut to open the park. Berdymukhamedov was not at the ceremony.

The park features a large marble arch with a huge portrait of Berdymukhamedov wearing a traditional Turkmen hat and tunic.

Controlling the world's fourth-largest natural gas reserves, Berdymukhamedov has used revenues from its exports to build marble-clad palaces across the desert nation of 5.5 million.

Modest wages are supplemented with subsidized gasoline and bread and there is free water, electricity and gas for the population. Critical voices are not heard.

Last week the U.S. State Department said in a global report on human rights in 2014, that Turkmenistan's biggest problems were arbitrary arrest, torture and disregard for civil liberties, including restrictions on freedoms of religion, speech, press and assembly.

Winding up his tour of Central Asia this month, U.N. Secretary-General Ban Ki-moon chose Ashgabat to warn local leaders that crackdowns on human rights in the mainly Muslim region could backfire by encouraging extremist ideologies.

(Writing by Dmitry Solovyov; Editing by Janet Lawrence)