DUBAI (Reuters) - Saudi King Abdullah left hospital Saturday after back surgery and will continue treatment at a royal clinic, the Royal Court said in a statement carried by the official SPA news agency.

"The Custodian of the Two Holy Mosques, King Abdullah bin Abdulaziz al-Saud ... left the King Abdulaziz Medical city this Saturday evening ... after God graced him with health to continue treatment in the clinic of his palace," it said.

The announcement came after King Abdullah's younger brother Crown Prince Sultan died of cancer in New York earlier on Saturday.

King Abdullah, who is in his late 80s, had a successful operation to tighten the ligaments around his third vertebra on Monday.

The Saudi line of succession does not move directly from father to eldest son, but has moved down a line of brothers born to the kingdom's founder King Abdulaziz Ibn Saud, who died in 1953.

The next-in-line after Sultan is assumed to be Prince Nayef, the interior minister since 1975, who is in his late 70s and has a reputation as more conservative than his elder brothers.

Nayef was made second-deputy prime minister in 2009 and has assumed day-to-day control of the kingdom before, during concurrent absences of his two elder brothers Abdullah and Sultan.

King Abdullah has given Saudi backing to U.S.-led efforts to confront and constrain Islamist militant groups, including al Qaeda, and has pushed Washington to support greater rights for Palestinians.

The monarch has introduced cautious reforms since becoming king in 2005.

He has brought about changes aimed at liberalizing the economy, giving greater technical, rather than religious, emphasis to education and allowing women more rights.

In the energy sector, King Abdullah is seen to have supported a moderate oil policy, raising production to prevent price spikes during supply outages from other countries.

A key U.S. ally, the top OPEC producer holds more than a fifth of world oil reserves and is the birthplace of Islam.

(Editing by Andrew Roche)