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 May 29 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.
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.