Kuala Lumpur: At least two people died and 18 others were missing after an overloaded fishing boat carrying illegal Indonesian immigrants capsized off the coast of southern Malaysia, a maritime official said on Tuesday.

The small fiberglass boat overturned and sank late on Monday 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.

He said the bodies of one man and a woman had so far been recovered.

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.

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.

Authorities have stepped up patrols along the country's long coastline during Ramadan as many from Indonesia seek to sneak out and return in rickety boats to celebrate Eid al-Fitr in late July, Islam's biggest festival which marks the end of the fasting month.

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.

The boats were also carrying Indonesians, trying to sneak out of the country for Ramadan.

Both Malaysia and Indonesia are Muslim-majority Southeast Asian countries.

About two million foreigners are estimated to live in Malaysia illegally, in addition to almost two million legal foreign workers.

Malaysia also draws refugees from strife-hit regional countries, such as Myanmar and Sri Lanka, who arrive illegally and hope to be resettled to the US, Australia or another nation that accepts them.