Riyadh separately announced that two of its oil tankers, apparently among the four, were "sabotaged" off the coast of Fujairah.
No one was killed in the attacks, Saudi Aramco, the kingdom's national oil company, said.
Describing Pompeo's talks with his European counterparts, Hook said they had discussed "what seemed to be attacks on commercial vessels". And Iran looks like it's being backed into a corner.
In his statement, al-Falih said the attacks on the two tankers happened at 6am on Sunday.
This is not the first time the Houthis have used drones.
Observers warned the United States is hurtling down the same path that led to the disastrous invasion of Iraq 16 years ago following a report late Monday that President Donald Trump reviewed a plan to send 120,000 ground troops to the Middle East if Iran launches an "attack" on American forces or moves to develop nuclear weapons. He said there will be no negotiations on a new nuclear deal.
Saudi Arabia says it was forced to shut down a key pipeline connecting the country's oil-rich east to a Red Sea port on Tuesday after two pumping stations came under attack by armed drones, with the country's oil chief blaming Iran for the incident.
Falih said the attack aimed to undermine maritime freedom and the security of oil supplies.
The crew was unharmed and the ship was in no danger of sinking, it said.
One of the pumping stations that was hit was about 700 kilometers (435 miles) from the Yemeni border. It was built during the Iran-Iraq war during the early 1980s, but was later converted to natural gas.
Meanwhile, the USA has warned it would take military action if Iran acted upon a threat to close the Strait of Hormuz, a strategic energy choke point through which millions of barrels of oil pass through each day.
The two Saudi ships were among the four vessels reportedly sabotaged in the Gulf of Oman, off the eastern coast of the UAE near the port city of Fujairah. A video report by Abu Dhabi's Sky News showed the hull of one vessel, the Andrea Victory, appearing to be twisted in one area from an impact at the waterline, though it was unclear exactly what had occurred.
Last week, Washington announced the deployment of an aircraft carrier battle group and a bomber task force to the Persian Gulf to counter what USA officials called "clear indications" of Iranian threats to the interests of the United States or its allies in the region.
The U.S. has recently warned ships that "Iran or its proxies" could be targeting maritime traffic in the region. Last week, the United States dispatched USS Abraham Lincoln, an aircraft carrier, and B-52 bombers into the Arabian Gulf.
On a trip to Russia, Secretary of State Mike Pompeo declined to comment on the report during a news conference in Sochi with Russian Foreign Minister Sergey Lavrov, but did say "we do not seek war with Iran". "We had formerly anticipated that they would carry out these sorts of activities to escalate tension".
The United Nations called on all sides to "exercise restraint for the sake of regional peace". In response, lawmakers in Tehran declared USA troops terrorists and called the US a state sponsor of terrorism. The U.S. knows that war won't benefit it and the only option for the Iranian people is resistance, Khamenei said at a meeting with senior officials, Tasnim reported.
Such drones remain hard to shoot down with either light or heavy weapons.