Yemen's Iran-aligned rebels seized a Saudi-flagged tug and two South Korean vessels at the weekend, the insurgents and Seoul officials said on Tuesday.
The incident follows a lull in Huthi attacks on Saudi Arabia as one Riyadh official said the kingdom had established an "open channel" with the rebels in a bid to end the four-year conflict.
The Huthis acknowledged they had seized three ships, including a Saudi one, in the Red Sea a few miles off Uqban island, west of the rebel-held capital Sanaa.
Seoul's foreign ministry said a South Korean dredger was being towed by one Korean and one Saudi-flagged tug when they were seized by the Huthis. It added that a total of 16 crew, two of them South Korean, had been taken to the Red Sea port of Saleef, where they were being held by the rebels.
"All of our citizens... are healthy and safe," ministry officials said in a statement.
"We are doing our very best for the early release of our citizens." Seoul has sent the South Korean navy ship Cheonghae, which had been on anti-piracy standby off the coast of Oman, to waters near where the incident took place.
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The Saudi-led military coalition backing Yemen's internationally recognised government accused the rebels of "hijacking" the Rabigh-3, which a global tracking website described as a Saudi-flagged vessel.
The rebels on Tuesday said the three ships were seized off Uqban island after they entered "territorial waters without prior notice", according to a statement carried by their Al-Masirah television channel.
The ships were taken to Saleef, it added, without disclosing the nationalities or number of crew members.
The Huthi rebels have been fighting the government and its allies for more than four years in a war that has pushed the country to the brink of famine.
A year after the Huthis seized Sanaa, Saudi Arabia, the United Arab Emirates and their allies intervened in the conflict in support of President Abedrabbo Mansour Hadi.
Since 2015, tens of thousands of people -- most of them civilians -- have been killed in a conflict that has triggered what the United Nations has described as the world's worst humanitarian crisis.
Earlier this month, a senior Saudi official raised hopes of possible de-escalation after he said Riyadh had an "open channel" with the rebels with the goal of ending the conflict.