South Korea's foreign ministry said a Korean dredger had been seized on Sunday evening, along with a Korean tugboat and a Saudi tugboat. It said 16 sailors including two South Koreans had been detained.
The Saudi-led coalition fighting against the Houthis said the seized vessels included a Korean drilling rig and the Saudi tug, the Rabigh 3, which was captured by armed Houthi fighters who attacked from two boats.
The incident is the latest at sea around Yemen, where Saudi Arabia is leading a coalition of Arab states fighting against the Houthis who control the capital and most population centers. The Houthis have been accused of attacking shipping in the past.
The Saudis say the Houthis represent a threat to one of the world's most important maritime trade routes. The Houthis say the coalition has imposed a blockade that threatens Yemenis with starvation.
Mohammed Ali al-Houthi, a senior Houthi official told Reuters the group's forces had seized a "suspect vessel" in the Red Sea and said the crew were being treated well.
"Yemeni coast guards ... are checking to see whether (the vessel) belongs to the countries of aggression or to South Korea, in which case it will be released after completing legal procedures," he said.
The dredger and the Korean tugboat were owned by South Korean builder Woongjin Development, a company official told Reuters.
Refinitiv ship tracking data shows the Saudi tug, the Rabigh 3, had recorded its destination as Jeddah in Saudi Arabia. Its current signal status was "restricted maneuverability." Its registered owner is Saudi Arabia's petrochemicals company PetroRabigh.
The Houthi coast guard, part of the movement's interior ministry, said in a statement three vessels had been seized near Uqban island, including one belong to Saudi Arabia, and taken to the Yemeni port of Salif. The statement said the vessels had been in Yemeni territorial waters without approval.
The Saudi-led coalition spokesman said the seizure was a "terrorist operation" that posed a threat to the freedom of international navigation and world trade.
The Saudi-led alliance intervened in Yemen in March 2015 against the Houthis after the group ousted the government from power in the capital Sanaa.
Houthi forces have been driven away from most of Yemen's coast over the course of the conflict but still hold Hodeidah, the country's biggest Red Sea port and base of the group's navy.The United Nations says the Houthis attacked two oil tankers last year in the Bab al-Mandeb strait at the southern mouth of the Red Sea, as well as a vessel carrying wheat to Yemen.