The small fibreglass boat overturned and sank late yesterday with around 80 people onboard as a patrolling vessel was pursuing it off the state of Johor, the official with the Malaysian Maritime Enforcement Agency said.
"The boat carried illegal immigrants going back to Indonesia" to celebrate the end of Ramadan, the official told AFP, adding that 59 people had been rescued.
"The boat was small and... Overloaded," said the official, who requested anonymity as he was not authorised to speak to the media.
The boat was heading to Indonesia's Batam island and sank three nautical miles off Tanjung Piai, peninsular Malaysia's southern-most point, he added, raising hopes that some of those missing could have swum to safety.
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He said authorities were still investigating the accident but the boatman - who is among those still missing - may have panicked when he saw the agency's patrol vessel and lost control.
He denied local media reports that the two vessels collided.
Boat accidents are common as Malaysia draws hundreds of thousands of illegal immigrants from poorer regional countries who fill factory, plantation, construction and other mostly low-paid jobs shunned by locals.
The government needed to crack down on agents and employers profiting from illegal labour and corruption among border authorities, said Aegile Fernandez, an official with Malaysian migrant labour rights group Tenaganita.
"Unless all this is addressed, this will happen again and again," she told AFP.
More than a dozen people died and about two dozen others went missing last month in two boat accidents in rough weather off Malaysia's west coast.
Both Malaysia and Indonesia are Muslim-majority Southeast Asian countries.