"We would also like to take this opportunity to extend our sincere condolences to the people of Saudi Arabia, and the Muslim world. May God`s mercy be upon him," it said.
The national flag will be flown at half-mast across Turkey and at foreign delegations on Saturday, it added.
Crown Prince Salman bin Abdulaziz has been declared as the new king of the oil-rich Gulf monarchy and Prince Muqrin bin Abdulaziz as the new Crown Prince.
Abdullah was recently admitted to hospital and placed on a ventilator after he was diagnosed with pneumonia.
Abdullah had undergone back surgery in November 2012. Since then, he refrained from attending events outside the kingdom, including a recent high-profile Gulf summit held in the Qatari capital, Doha.
Salman, 79, is a half-brother of the deceased king. He was appointed crown prince in June 2012 after the death of the late crown prince, Naif.
Muqrin is also a half-brother of Abdullah and the youngest son of the founder of Saudi Arabia. He was serving as second deputy prime minister and the king`s special envoy.
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