The Saudi-led coalition fighting Yemen's Huthi insurgents has launched air strikes targeting the rebel-held capital Sanaa after a deadly attack against coalition ally Abu Dhabi.

"In response to the threat and (out of) military necessity, air strikes have begun in Sanaa," the official Saudi Press Agency said on Twitter.

The Huthis' Al-Masirah TV channel confirmed the raids by the coalition, without immediately reporting any casualties.

Yemen's Huthi rebels have claimed responsibility for a deadly attack in Abu Dhabi, claiming to have targeted "a number of important and sensitive Emirati sites and installations".

The United Arab Emirates vowed reprisals after a missile and drone attack triggered a fuel tank blast that killed three people in the city.

"The armed forces carried out... a successful military operation within the framework of an operation named Yemeni Hurricane," Huthi military spokesman Yahya Saree said in a statement broadcast on the rebels' Al-Masirah TV channel.

He went on to urge civilians and foreign firms to "stay away from vital installations" in the UAE after claiming deadly attacks in Abu Dhabi.

"We warn foreign firms, the citizens and residents of the UAE that they should stay away from vital installations for their own security," the spokesman said.

The UAE is part of a Saudi-led military coalition that supports Yemen's government against the Iran-backed Huthi rebels, who have repeatedly targeted Saudi Arabia with cross border strikes.

But this is the first deadly assault on UAE soil.

Two Indians and a Pakistani working for oil giant ADNOC died as three petrol tanks exploded near a storage facility, while a fire also ignited in a construction area at Abu Dhabi airport in the heart of the UAE, a renowned safe haven in the volatile Middle East.

Police in Abu Dhabi said "small flying objects, possibly belonging to drones" were found at both sites.

Drone attacks have been a hallmark of the rebels' assaults on neighbouring Saudi Arabia.

"We condemn the Huthi terrorist militia's targeting of civilian areas and facilities on UAE soil today... this sinful targeting will not go unpunished," UAE Foreign Minister Abdullah bin Zayed Al-Nahyan said in a statement, as his ministry described the attack as a "heinous criminal escalation".

The US, Britain and France have all strongly condemned the attack in Abu Dhabi.

"The Huthis have claimed responsibility for this attack and we will work with the UAE and international partners to hold them accountable," National Security Advisor Jake Sullivan said in a White House statement.

"Our commitment to the security of the UAE is unwavering and we stand beside our Emirati partners against all threats to their territory," he added.

"I condemn in the strongest terms the Houthi-claimed terrorist attacks on the United Arab Emirates," Britain's Foreign Secretary Liz Truss tweeted.

"These attacks threaten the security of the United Arab Emirates and regional stability," France's Foreign Minister Jean-Yves Le Drian said.

"France expresses its support for the UAE in the face of these attacks," he said.

Mr Le Drian reiterated his call for the Huthis to "immediately cease their destabilising actions in Yemen and in the region and to engage constructively in a political process for exiting the crisis".

"France reaffirms its mobilisation in favour of a cessation of hostilities in the whole country and a relaunch of talks with a view to a global political agreement under the aegis of the United Nations," the minister said.

The incident follows a surge in fighting in Yemen including advances by UAE-trained troops.

The rebels also seized a UAE-flagged ship and its international crew earlier this month.

Saudi Arabia, Bahrain, Qatar and the Organisation of Islamic Cooperation all condemned the "terrorist" attack.

Eight Huthi drones targeting Saudi Arabia were also intercepted, the coalition said.

Fake drones set up by the Houthis in a fountain in Yemen

The rebels have previously threatened to target Abu Dhabi and Dubai, the gleaming crown jewels of the UAE which last year opened its first nuclear power plant.

Huthi military spokesman Yahya Saree tweeted that the rebels' armed forces would "announce special military operation(s) in depth of UAE in the coming hours".

'Clear warning'

Abdul Ilah Hajar, adviser to the president of the Huthis' Supreme Political Council in Sanaa, said it was a warning shot from the rebels.

"We sent them a clear warning message by hitting places that are not of great strategic importance," he told AFP.

"But it is a warning if the UAE continues its hostility to Yemen, it will not be able in the future to withstand the coming strikes."

Saudi Arabia's foreign ministry condemned "in the strongest terms the cowardly terrorist attack" while Bahrain and Qatar also slammed the strikes.

The incident comes two weeks after the rebels hijacked the UAE-flagged Rwabee and released footage purporting to show military equipment on board.

The UAE said the Rwabee, whose 11 crew are now hostages, was a "civilian cargo vessel" and called the hijacking a "dangerous escalation" in the busy Red Sea shipping route.

The rebels later rejected a UN Security Council demand for the ship's immediate release, saying it was "not carrying... toys for children but weapons for extremists".

Yemen's conflict has been a catastrophe for millions of its citizens who have fled their homes, with many on the brink of famine, in what the UN calls the world's worst humanitarian crisis.

The UAE joined the coalition against the Huthis before announcing a change of tack in 2019.

The pro-government Giants Brigade troops, backed by the Saudis and UAE, recently delivered a significant blow to the rebels by recapturing three districts in Shabwa governorate.

The clashes were part of an upswing in violence in the shattered country, where the war is being fought on several fronts.