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"We have heard from the authorities here that two Indians died," India's envoy to the UAE Sunjay Sudhir told NDTV. "We are trying to find out their identities. We will reach out to their families... Stay calm. The UAE is a very peaceful place," Mr Sudhir said.
Saudi Arabia's foreign ministry condemned "in the strongest terms the cowardly terrorist attack" while Bahrain also slammed the "terrorist Huthi militia's launch of a number of booby-trapped drones".
Yemen's Iran-aligned Houthi movement said it carried out the attack on the UAE, according to reports. On Twitter, some people posted what appeared to be the site of the explosion, showing a thick plume of black smoke rising high into the sky.
Earlier, local media had reported that three fuel tanks exploded near depots of Abu Dhabi National Oil Company, but the cause was not immediately known.
Houthi military spokesman Yahya Saree later told the broadcaster, Almasirah, that they would soon give details of their "military operation in UAE territory".
The incident in Abu Dhabi comes just days after a UAE ship was seized by the Houthis. The United Nations Security Council has condemned the seizure and demanded immediate release of the vessel and crew.
Yemen has been engulfed in a conflict between government forces led by President Abdrabbuh Mansour Hadi, and the Houthi rebels. Since March 2015, a Saudi-led Arab alliance working with Mr Hadi's forces has been conducting air, land and sea operations against the Houthis.
The Saudi-led coalition believes the use by Houthi forces of two ports as military bases would turn them into legitimate military targets, coalition spokesman Brigadier General Turki al-Malki said last week.
The ports of Hodeidah and Salif are controlled by Yemen's Iran-aligned Houthi movement and which the Saudi-led coalition has said uses them as launching points for missiles, drones and marine operations.
However, air and sea access to Houthi-held areas is controlled by the Saudi-led coalition, that intervened in Yemen in early 2015 after the movement ousted the internationally recognised government from the capital Sanaa.
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