The report comes at a time of heightened tension in the region and a day after Saudi Arabiasaid two of its oil tankers came under attack off the coast of the United Arab Emirates.
Brent crude futures were at $71.02 a barrel at 1335 GMT, up 79 cents or 1.12 per cent. Authorities have yet to reveal the extent of the damage to the Saudi tankers, although initial reports suggestedAl Marzoqah's main engine caught fire. Saudi Arabia's state run Saudi Press Agency described it as "a sabotage attack".
Chris Ghika told Pentagon reporters that the Iran-backed groups are one of many threats faced by the coalition, but said there has been no increase in the dangers they pose.
Iranian President Hassan Rouhani hit back, saying the Islamic republic was "too great to be intimidated by anyone". "They are not going to be happy people".
The country's energy minister said he condemned Monday's attack as well as the recent attack on four tankers in the Arabian Gulf off the coast of the UAE on Sunday night.
This is not the first time the Houthis have used drones.
The US administration re-imposed sanctions on Iranian oil exports in November after President Donald Trump unilaterally pulled out of the 2015 nuclear deal between Tehran, Washington and five other countries. He said there will be no negotiations on a new nuclear deal.
The Saudi statement came just hours after Iranian and Lebanese media outlets aired false reports of explosions at Fujairah's port. Emirati officials have declined to elaborate on the nature of the sabotage or say who might have been responsible.
Falih said the attack aimed to undermine maritime freedom and the security of oil supplies.
In Europe, there are concerns that the USA and Iran could stumble into a military confrontation.
A fifth of global oil consumption passes through the strait from Middle East crude producers to much of the world. The broadcast only showed one side of the ship, which bore no signs of damage, describing it as the closest one to shore in Fujairah.
A US official in Washington, without offering any evidence, told the AP that an American military team's initial assessment indicated Iran or Iranian allies used explosives to blow holes in the ships. The official was not authorized to discuss the investigation and thus spoke on condition of anonymity. "However, Iran's default option for 40 years has been violence, and we are ready to defend USA personnel and interests in the region".
"Four commercial ships were subjected to sabotage operations today, 12 May, near UAE territorial waters in the Gulf of Oman, east of Fujairah", the Ministry of Foreign Affairs and International Cooperation said in a statement carried by state news agency WAM.
Underscoring the worldwide concern, German Foreign Minister Heiko Maas said he used his one-on-one with Pompeo to stress that "we are concerned about the development and the tensions in the region, that we do not want there to be a military escalation".
United Nations deputy spokesman Farhan Haq called on "all concerned parties to exercise restraint for the sake of regional peace, including by ensuring maritime security".
The USS Abraham Lincoln sails south in the Suez canal near Ismailia toward the Persian Gulf, May 9, 2019.
"It's not in [Iran's] interest, it's not in our interest, it's not in Saudi Arabia's interest to have a conflict".
The Houthis have been selected by Iran as a good place to test out the drone capabilities against a Western-backed army like the Saudis who use US and other Western equipment.
Such drones remain hard to shoot down with either light or heavy weapons.