Malaysia has continued to reject taking in more migrants stranded on boats off Southeast Asia's shores, despite growing international pressure.

The Southeast Asian nation is in high-level talks with its neighbours to try to solve the refugee crisis after boats holding more than 2,000 migrants, including many Rohingya Muslims and Bangladeshis, landed in Indonesia, Malaysia and Thailand in recent weeks.

Malaysian Foreign Minister Anifah Aman met on Sunday with his counterpart from Bangladesh, Abul Hassan Mahmood Ali, ahead of a meeting with the Indonesian and Thai foreign ministers scheduled for Wednesday, officials said.

"I have already stated that we cannot afford to accept more of them, as a huge number already exist here - and so far no countries want to settle them," Aman was quoted as saying after Sunday's talks by the online edition of Malaysia's government-linked mass daily New Straits Times.

"We have to look at our own interests too, our social problems and security problems - we have to take that into consideration," Anifah said.

"We are asking Myanmar to participate in finding a solution," he added.

Thailand and Indonesia have also refused to allow the migrants - most of whom are ethnic Rohingya Muslims facing persecution in Myanmar - to enter their waters.

Al Jazeera spoke to stranded migrants in waters off Thailand. One of the migrants said that "people were starving and suffering from diarrhoea and were dying because they did not have food to eat or clean water".

Many aboard said they wanted to go to Malaysia where their family members were.

Aid groups estimate that thousands more are stranded at sea after a crackdown on human traffickers prompted captains and smugglers to abandon their human cargo.

Desperate and hungry

There appears to be no quick solution to the crisis, especially since Myanmar appears unwilling to engage in discussions and refuses to accept any responsibility over the migrant crisis.

Navy ships from Malaysia, Thailand and Indonesia have in recent days intercepted boats packed with desperate, hungry migrants, giving them food and water and sending them away - a move that prompted international outrage.

An increasingly alarmed UN has warned that pushing the boats away could create a crisis of "floating coffins" and urged regional leaders to put human lives first.

Malaysia, the current chair of the 10-nation Association of Southeast Asian Nations, or ASEAN, is also the desired destination for most of the migrants.

The Muslim-majority country has hosted more than 45,000 Rohingya Muslims over the years.

Myanmar's cooperation is seen as vital to solving the crisis, but its government has already cast doubt on whether it will attend a conference to be hosted by Thailand on May 29 that is to include 15 Asian nations affected by the emergency.

"We are not ignoring the migrant problem, but our leaders will decide whether to attend the meeting based on what is going to be discussed," Zaw Htay, director of the office of Myanmar's president, said on Saturday.

"We will not accept the allegations by some that Myanmar is the source of the problem."

He directed some of the blame on Myanmar's neighbours, saying that from a humanitarian point of view, "it's sad that these people are being pushed out to sea by some countries".