The HTMS Sukhothai sank after water flooded its power controls on Sunday night.
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The Navy authorities said they had rescued 75 crew, but 31 sailors were still missing.
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"It's been more than 12 hours, but we will keep looking," a navy spokesman told the BBC
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Search crews worked through the night to find survivors.
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Also continuing on Monday with air force assistance.
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The navy also announced an investigation into the cause of the disaster.
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Officials said the ship went down after it took on water,
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Officials said the ship short-circuited its power room.
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The power lost before sinking around 23:30 local time Sunday.
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The ship had been on a patrol 32km (20 miles) east of Bang Saphan,
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Back-up rescue ships trying to find survivors in choppy waters.
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Three naval ships and helicopters were sent to assist.
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Only the HTMS Kraburi reached the vessel before it sank.
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Prime Minister Prayut Chan-o-Cha released a statement on Monday.
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"I am following the news closely - about five people are seriously injured," he said.
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The HTMS Sukhothai was built for the Thai navy in the US in the mid-1980s.
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