Dr Anwar Gargash, diplomatic adviser to President Sheikh Khalifa, described the group as a “terrorist militia” after two blasts in the capital.
Two Indians and a Pakistani died when a device hit three fuel lorries at Adnoc's petroleum storage unit in the ICAD industrial area of Mussaffah at about 10am. Six people suffered mild to moderate injuries.
Officials said an investigation was ongoing but that the blasts may have been caused by aerial drones.
“The tampering of terrorist militias with the stability of the region is too weak to affect the journey of security and safety that we live in, and the fate of this reckless absurdity will be demise and defeat.”
Fires caused by the blasts on Monday morning were brought under control by emergency crews, police said.
At Abu Dhabi airport, a device caused a small fire in an under-construction extension. It is understood the terminals were not affected or damaged.
The Ministry of Foreign Affairs and International Co-operation said in a statement that it “reserves the right to respond to these terrorist attacks and this sinister criminal escalation".
It condemned the “terrorist militia’s targeting of civilian areas and facilities on UAE soil today” and said its thoughts were with those who died in the strike.
UN chief Guterres condemns 'attacks on civilians'
In New York, UN Secretary General Antonio Guterres condemned the attack.
The strikes “reportedly caused several civilian casualties and have been claimed by the Houthis,” said UN spokesman Stephane Dujarric.
“Attacks on civilians and civilian infrastructure are prohibited by international humanitarian law.”
He urged the Houthis, pro-government and coalition forces fighting in Yemen's protracted conflict to “exercise maximum restraint” and engage in an UN-led peace process.
“There is no military solution to the conflict in Yemen,” said Mr Dujarric.
US, Britain and Arab allies condemn strikes
White House National Security Adviser Jake Sullivan condemned the terrorist attacks on Monday and promised a co-ordinated response. US Secretary of State Antony Blinken called his Emirati counterpart Sheikh Abdullah bin Zayed, and the UK's foreign secretary Liz Truss tweeted a public condemnation.
Saudi Arabia, Bahrain, Oman, Qatar, Kuwait, Lebanon, Jordan and Iraq were among the Arab nations to condemn the attacks and express solidarity with the Emirates. The Arab League and Gulf Co-operation Council also voiced their condemnation.
Bahrain's Foreign Ministry said the group had attacked “vital civilian facilities” in an unprovoked strike, while Oman's Foreign Ministry offered solidarity with the UAE, and “support for measures it takes to protect its security and stability".
Saudi Arabia's government said the strikes were a “terrorist act” by a group that threatened stability in the region.
“The kingdom stressed that it continues to confront all attempts and terrorist practices of the Houthi militia through its leadership of coalition forces to support legitimacy in Yemen,” it said.
Adnoc 'deeply saddened' by loss of employees
Adnoc, for whom the three dead and six injured people worked, said in a statement: “At approximately 10am this morning, an incident occurred at our Mussaffah Fuel Depot in Abu Dhabi which resulted in the outbreak of a fire.
“Emergency response teams, including civil defence, fire and ambulance responders as well as an Adnoc emergency response team quickly attended the scene, and the fire was brought under control and extinguished.
“Adnoc is deeply saddened to confirm that three colleagues have died. A further six colleagues were injured and received immediate specialist medical care.
“Professional support teams are supporting the families of all those who have been affected.
“At this time, the entire Adnoc family extends its deepest sympathy to the family and friends of our colleagues who died this morning.
“We are working closely with the relevant authorities to determine the exact cause and a detailed investigation has commenced.”
Etihad Airways said there was limited disruption to flights. Services soon resumed as normal.
“Following an incident in the construction area of Abu Dhabi Airport earlier this morning, precautionary measures resulted in a short disruption for a small number of flights. However, normal airport operations were quickly resumed,” a representative said.
“The safety and comfort of our guests and crew is our number one priority.”
Sunjay Sudhir, India’s ambassador to the UAE, said his government would provide “whatever assistance is possible” to the family of the two deceased Indian citizens. Pakistan's Foreign Ministry expressed its condolences and said it would support the family of the Pakistani who died in the Mussaffah blast.
Recent Houthi losses
The Houthis, who ousted Yemen's internationally recognised government in 2014, have recently suffered heavy losses to pro-government and Saudi-led coalition forces.
In the oil-rich Shabwa province, 40 were killed 10 days ago when fighters from the Southern Transitional Council seized a military base, while as many as 280 died in air strikes on Marib and Al Bayda at the weekend, the coalition said.
The Houthis continue to hold much of the country's north-west, where the bulk of the Yemeni population is concentrated, including the capital Sana'a and Marib.