* Morocco quit AU in 1984 over Western Sahara sovereignty
* Wants to give the territory autonomy under Moroccan flag
* AU prefers referendum as solution to the conflict (Adds AU chairman comments)
By Aziz El Yaakoubi
RABAT, July 18 (Reuters) - Morocco has asked the African Union to readmit it to an organisation it left 32 years ago, as it seeks support for its plan to offer autonomy to the disputed territory of Western Sahara while keeping it under Moroccan sovereignty.
Morocco abandoned its seat in 1984 when the AU recognised the breakaway Western Sahara republic.
"It has been a long time that our friends have been asking Morocco to take back its seat in its natural institutional place, and now the time has come," Morocco's King Mohammed said in a letter to the AU, according to state news agency MAP.
The Sahrawi Arab Democratic Republic (SADR) was declared by the Polisario Front independence movement in the 1970s in the sparsely populated stretch of desert that was formerly a Spanish protectorate.
Morocco says at least 36 of the 54 AU member countries do not acknowledge the territory as a separate state and it is time to withdraw its recongition. None of the Western powers, nor the United Nations recognise the Sahrawi republic.
But it is unclear if powerful AU members including Algeria and South Africa, which have expressed support to hold a referendum of the people of Western Sahara on their sovereignty, would accept Morocco's request.
The AU chairman, Chadian President Idriss Deby, said he would like to see Morocco return to the regional body.
"Morocco has the right and the obligation to return to its great family when and how it wants," Deby told reporters on the margins of an AU summit in Kigali.
"Now I do not know if it (Morocco) posed conditions or not, and that is not important," he added.
Morocco has controlled most of the territory since 1975. The area has offshore fishing, phosphate reserves and oilfield potential. Moroccan officials visited Algiers, Abuja and Nairobi last week as the country seeks support for its autonomy proposal.
Rabat is also in talks with the United Nations about letting civilian staff of the Western Sahara peacekeeping mission MINURSO back into the country, after expelling them earlier this year when U.N. Secretary-General Ban Ki-moon used the word "occupation" to describe its 1975 annexation of the territory.
The U.N. mission was formed more than 20 years ago ahead of an expected referendum on the Western Sahara's political future that has never taken place.
In 2014, Morocco rejected the AU's decision to appoint a special envoy for the Western Sahara, saying the body had no legal authority to intervene. (Additional reporting By Clement Uwiringiyimana in Kigali; Editing by Aidan Lewis and Robin Pomeroy)