Indonesian police said passengers aboard one vessel carrying 712 people recounted how their boat sank off the east coast of the huge island of Sumatra after earlier being driven away by Malaysia.
Activists estimate up to 8,000 migrants are at sea in Southeast Asia.
But the decision by Indonesia, Malaysia and Thailand to turn away stricken boats filled with starving Bangladeshis and ethnic Rohingya from Myanmar has been met with outrage, including from the US and UN.
The boat, whose passengers included 61 children, was sinking but Indonesian fishermen ferried them to shore, he said.
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Forty-seven more people from another vessel were rescued not far down the coast after the hungry passengers leapt into the water pleading with local fishing boats to help them.
Nearly 1,300 migrants are already sheltering in Aceh after managing to get ashore in recent days.
The boat's passengers included many children and women who wept as they begged for food and water, after arriving near the southern Thai island of Koh Lipe on Thursday.
They told a boatload of journalists of a grim two-month odyssey in which 10 passengers had died of starvation or illness and were tossed overboard.
"We haven't had anything to eat for a week, there is nowhere to sleep... My children are sick," said Sajida, 27, a Rohingya who was travelling with her four young children.