Nearly 3,000 people on boats from Myanmar and Bangladesh have been rescued or swum to shores in Malaysia, Indonesia and Thailand.
Several thousand more are believed to be trapped on boats at sea with little food or water in a crisis sparked by smugglers abandoning human cargo after a supposed Thai crackdown on the trade.
UN refugee agency believes an estimated 25,000 Rohingya and Bangladeshi people have taken to boats in the first three months of this year, double the number in the same period in 2014.
The following is a regional summary of the current "boat people" crisis:
More than 1,100 migrants have washed ashore in Malaysia over the past week after people-smuggling gangs dumped migrants in shallow waters off the coast of the resort island of Langkawi.
Some migrants swam to shore after harrowing month-long journeys at sea, crammed in with hundreds of other people and few supplies.
Malaysia's Prime Minister Najib Razak has joined Thailand in calling on Myanmar, from where many boats carrying migrants from the persecuted Rohingya minority originate, to help address the burgeoning "humanitarian catastrophe".
Myanmar has so far refused to acknowledge its role in the crisis.
Around 1,500 migrants have been intercepted by Indonesian authorities or plucked from the sea, many in a desperate condition.
On Friday, around 900 Bangladeshis and Rohingya migrants were rescued from sea after their boat sank off the eastern coast of Sumatra.
Survivors told stories of people being thrown overboard in fighting over dwindling food supplies. Some Bangladeshis on board said they had been kidnapped and taken to sea.
Last Sunday, Indonesian authorities intercepted a boat off the coast of northwestern Aceh province, rescuing more than 600 migrants.
A second vessel carrying about 400 migrants was spotted the following day by Indonesian navy vessels. The boat was damaged but afloat and its captain had fled.
Indonesia's navy provided the boat with fuel and then towed it out of their waters, declining to say if it was heading to Malaysia, its suspected destination.
On Thursday, a boat carrying an estimated 300 Rohingya migrants was found adrift several kilometres off the Thai tourist resort of Koh Lipe.
Authorities dropped food and water into the sea from a helicopter, prompting a desperate scramble to retrieve the packages.
Some of the visibly-weak migrants said they wanted to go to Malaysia and the Thais fixed their broken engine and pointed them south.
However, the boat was still drifting on Saturday in between Thai and Malaysian waters, with neither country seemingly keen to let them make shore.
On Friday, around 100 migrants from a separate boat made it to land in southern Thailand.
Advocacy groups believe there may be several other boats in the vicinity, with human smugglers believed to be among the passengers.
Since May 1, some 250 migrants from Bangladesh and Myanmar have been found in jungle camps in the southern Thai province of Songkhla, bordering Malaysia.
Bay of Bengal
Coastal towns along Bangladesh's Cox's Bazaar district and Myanmar's Rakhine State are the starting point for most migrant journeys.
A trawler with 116 Malaysia-bound migrants was found adrift off a small island near Myanmar's border.
Small vessels carry migrants out to larger "cargo" boats moored in international waters, which head towards southeast Asia when full.
Chris Lewa of Arakan Project, an advocacy group for the rights of Rohingya, said her contacts had told her five cargo vessels heading east had left in early May.
"These boats usually carry between 250-800 people. So there could be at least another 1,000 on their way," she said.
Two remain moored in the Bay of Bengal but are not thought to be taking on any more people at the moment, she added.
Police have killed several key players in the trade while dozens of lower level smugglers have been rounded up.