Sheikh Rashid bin Hamad al-Sharqi, 31, is the second son of the emir of Fujairah, one of the seven monarchies making up the United Arab Emirates.
He arrived in Doha on May 16, the report said.
Abu Dhabi is the capital and richest emirate of the UAE.
Speaking to the New York Times, Sheikh Rashid accused Emirati rulers of blackmail and money laundering but did not offer evidence to back up his claims.
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He also spoke of tensions within Emirati elites over the UAE's commitment of troops in the war in Yemen.
Sheikh Rashid said there had been more UAE war deaths than the 100 that have been reported publicly and said "there have been more deaths from Fujairah than anywhere else".
An Emirati official contacted by AFP declined to comment, but UAE minister for foreign affairs Anwar Gargash made a veiled reference on Twitter to "conspiracy against this or that ruling family by those who lack courage and instead resort to leaks and interviews".
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Along with Saudi Arabia, Egypt and Bahrain, the United Arab Emirates cut all ties with Qatar in June 2017, accusing Doha of supporting Islamist groups and being too close to Gulf archrival Iran.
Qatar, the world's largest exporter of liquified natural gas, denies the accusations.
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The New York Times report said that Sheikh Rashid appeared to be the first time in the UAE's nearly 47-year history that a member of one of its seven royal families had publicly criticised its rulers.
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