The U.N. has warned the situation could develop into a "massive humanitarian disaster".
The wooden boat towed back out to sea by the Thai navy was found on Thursday near the southern Thai island of Koh Lipe in the Andaman sea with hundreds of migrants packed on the deck, including children.
Thai authorities fixed the boat's engine and supplied those on board with food, water and medicine before towing it back out to sea in the early hours of Friday morning, said Lieutenant Commander Veerapong Nakprasit, a naval officer based on Koh Lipe.
"Those on the boat did not want to come to Thailand so we gave them food, medicine, fuel and water," Veerapong told Reuters.
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"We did our humanitarian duty. They wanted to go to a third country. They did not want to come to Thailand so we sent them on their way. This is not a push back because these people wanted to go."
Veerapong said the boat was without a captain but that some of those on board had been trained by local Thai fishermen to navigate.
"They trained for around three hours until they knew how to steer. They were really very good," he said, adding that a radar station on the island monitored the boat until it entered international waters.