CAIRO, Nov 23 (Reuters) - Egypt has asked Turkey's ambassador to leave and accused Ankara of backing unnamed organisations bent on spreading instability - a likely reference to the Muslim Brotherhood of ousted Egyptian president Mohamed Mursi.

Turkey said it would reciprocate within hours in the latest sign of a growing dispute between the two regional powers and U.S. allies, a row triggered by the Egyptian army's overthrow of Mursi on July 3.

Turkey has emerged as one of the fiercest international critics of Mursi's removal, calling it an "unacceptable coup". Mursi's Muslim Brotherhood, which has been staging protests calling for his reinstatement, has close ties with Turkey's ruling AK Party.

Ankara was "attempting to influence public opinion against Egyptian interests, supported meetings of organisations that seek to create instability in the country," said foreign Ministry Spokesman Badr Abdelatty on Saturday.

In response to Egypt's decision, Turkish President Abdullah Gul spoke live on state run TRT television saying, "I hope our relations will again get back to its track."

But a Turkish foreign ministry spokesman said Ankara was in touch with the ambassador "and we will respond with reciprocal steps in coming hours".

Both sides had recalled their ambassadors in August for consultation after Egyptian security forces stormed into pro-Mursi camps on August 14, killing hundreds. (Reporting by Asma Alsharif and Ali Abdelatty, and Seda Sezer in Turkey.; Editing by Andrew Heavens)