Myanmar's government has said it is not responsible for the migrant boat crisis in south-east Asia, and may not attend an emergency summit on the issue.
Thousands of migrants from Bangladesh and Myanmar are feared stranded in boats in the Andaman Sea after their crews deserted them.
Indonesia, Malaysia and Thailand have been turning away migrant boats.
Survivors have described desperate conditions on the boats, with people thrown overboard amid fights for food.
Rohingya Muslims have been leaving Buddhist-majority Myanmar, also known as Burma, because they are not recognised as citizens and face persecution.
Many of the Bangladeshis at sea are thought to be economic migrants.
The BBC's Jonah Fisher in Bangkok says there are at least five people-smuggling boats, carrying up to 1,000 migrants, moored just off the northern coast of Myanmar near the maritime border with Bangladesh.
The crackdown on boat people landing in Thailand and Malaysia means the smugglers are reluctant to make the journey but our correspondent says they are refusing to release those on board unless ransoms are paid.
Thailand is hosting a meeting on 29 May for 15 countries to discuss ways to address the crisis.
However, Zaw Htay, director of Myanmar's presidential office, said his leaders would not attend if the word "Rohingya" was used in the invitation, as they did not recognise the term.
"We are not ignoring the migrant problem, but... we will not accept the allegations by some that Myanmar is the source of the problem," he told the Associated Press news agency.
"The problem of the migrant graves is not a Myanmar problem, it's because of the weakness of human trafficking prevention and the rule of law in Thailand," he said in a separate interview with AFP.
At the scene: Jonathan Head, BBC News, southern Thailand
It is being called human ping-pong - the refusal of south-east Asian countries to accept mainly Rohingya migrants from Myanmar, and their navies' policy of pushing boats back into each other's territory.
So the boat we found on Thursday, which had already been pushed back once from Malaysia, into Thailand, was then pushed back again by the Thai navy. At the time of writing it lies just inside Malaysian waters. They tell us it will now be towed to a fourth country, perhaps Indonesia.
On board, more or less running the boat, are Rohingya brokers, who have good reason not to want to land in Thailand, where an anti-trafficking operation is underway.
Thai officers are negotiating with these men, who claim to speak for all 350 on board. So the Thais say they were merely helping by repairing the engine and sending the boat on its way.
But what about the women and children on board - more than half the passengers? What about all the visibly ill people, or those who look half-starved? How can an endless sea voyage in an appallingly cramped and unsanitary boat help them? Thai and Malaysian officials are not saying.
Close to 800 migrants were rescued after their boat sank on Friday near Langsa in Indonesia's Aceh province, after being pushed back from both Indonesia and Malaysia's coasts.
The boat had reportedly been at sea for two months and was recently deserted by its crew.
The Rohingya and Bangladeshi migrants on board began fighting over dwindling food supplies, survivors said.
"They were killing each other, throwing people overboard," Langsa police chief Sunarya told AFP.
Rohingya Muslims attempt to flee Myanmar every year during the non-monsoon season, but the smugglers who take them to Thailand have been scared by a recent Thai crackdown.
Instead they are reported to have been abandoned at sea. The numbers involved are unclear but rights group say thousands are thought to be stranded.
Who are the Rohingyas?
- Rohingyas are a distinct, Muslim ethnic group mainly living in Myanmar, which is also known as Burma
- Thought to be descended from Muslim traders who settled there more than 1,000 years ago
- Also live in Bangladesh, Saudi Arabia and Pakistan
- In Myanmar, they are regularly persecuted - subjected to forced labour, have no land rights, and are heavily restricted
- In Bangladesh many are also desperately poor, with no documents or job prospects