The Yemeni rebels, known as Houthis, have been clashing in the capital, Sanaa, for five consecutive days with supporters of Yemen's former president, Ali Abdullah Saleh, an ally turned adversary.
The alliance between the Houthis and Saleh had helped the rebels retain control of Sanaa, despite nearly three years of coalition airstrikes.
The Houthis accuse Saleh of striking deals with Saudi Arabia and the UAE. Since the recent clashes erupted in Sanaa, the Saudi coalition has been targeting the Houthis and backing Saleh's camp.
The Houthi claim Sunday came as the UAE celebrated its 46th National Day with public sector holiday that began on Thursday with a commemoration of the country's fallen soldiers.
In a statement posted on the UAE's state-run WAM news agency, authorities said: "The National Emergency and Crisis and Disasters Management Authority denies the claim that the Houthis fired a missile toward the country."
"The UAE possesses an air defense system capable of dealing with any threat of any type or kind," the statement added, saying that the nuclear power plant in Abu Dhabi was well-protected.
The National, a state-aligned newspaper in Abu Dhabi, also reported that Barakah's operations were "unaffected on Sunday, while sources on the ground confirmed there were no signs of an attack to the structure." The newspaper did not elaborate.
The $20 billion Barakah nuclear power plant, being built with help from South Korea, is near Abu Dhabi's border with Saudi Arabia. The plant lies some 225 kilometers (140 miles) west of the UAE capital.
The first of its four reactors is scheduled to come online in 2018. When fully built, officials hope the nuclear plant will provide up to 25 percent of all energy needs in the UAE, a federation of seven sheikhdoms on the Arabian Peninsula.
The UAE is a major U.S. ally that hosts some 5,000 American troops and is the U.S. Navy's busiest foreign port of call. The U.S. military declined to comment on the Houthi missile claims, other than to acknowledge being aware of them.
Like other U.S. Gulf allies in the region, the UAE has the Patriot Missile defense system capable of shooting down ballistic missiles and is the only international client to have on delivery the U.S.-made Terminal High Altitude Area Defense system.
The Houthis last month had targeted the Saudi capital, Riyadh, with a ballistic missile that was intercepted by Saudi air defenses. It was the deepest strike inside the kingdom since the war between the Saudi-led coalition and the Houthis and their allies began in March 2015.
For the Houthis to launch a missile from Yemen at the UAE, it would likely have to fly over Saudi Arabia's vast southeastern desert in order to reach Abu Dhabi.
Senior Houthi official Deif-Allah al-Shami told The Associated Press that the missile fired toward Abu Dhabi was a "message to the United Arab Emirates for its political and financial support to Saleh."
He said that the UAE has hosted members of Saleh's family, including his son who was an ambassador to the UAE and believed to be residing here during the conflict. Al-Shami also said the rocket attack was a message that "we will continue to target every nation that participated in the aggression against Yemen."
The UAE's forces have mostly focused on securing the southern region of Yemen, while Houthis control much of the north.
At least 100 Emirati soldiers have been killed in the war, which was launched to dislodge the Houthis from Sanaa after they overran the capital and kicked out the internationally-backed Yemeni government from power. The conflict has killed more than 10,000 Yemeni civilians and pushed millions to the brink of famine.
Both the U.S. and Saudi Arabia have accused its rival Iran of supplying Houthis with missiles, including the one used to target Riyadh on Nov. 4. Both the Houthis and Iran deny the claim.
Iran, meanwhile, has close trade ties with the UAE. In November, Iranian authorities ordered a two-day ban on a hard-line Iranian newspaper after it ran a headline saying the UAE's tourism hub of Dubai was the "next target" for Yemen's Houthi rebels.
Associated Press writers Maggie Michael in Cairo and Ahmed Al-Haj in Sanaa, Yemen, contributed to this report.
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