(CNN) Meetings between the foreign ministries of Indonesia, Thailand and Malaysia are taking place Wednesday in an effort to ward off a looming humanitarian disaster. Thousands of Rohingya migrants remain stranded in the Andaman Sea, while authorities around the region refuse to take them in.

The scale of the crisis is still unknown. No organization, from the UNHCR and the International Organization for Migration (IOM) to Rohingya rights groups, knows how many boats there are. The number of migrants stranded aboard these ships, however, is estimated to be in the thousands.

Despite a plea from U.N. Secretary General Ban Ki-moon, urging Southeast Asian leaders to uphold "international law" and "the obligation of rescue at sea," Malaysia, Thailand and Indonesia are currently refusing to accept the "boat people" -- men, women and children who remain on ships, with rapidly dwindling provisions.

Thailand supplied them with food and water in the middle of last week, the last confirmed resupply.

CNN understands that the ships, which remain at sea, are trying to elude patrols and the refugees are effectively being held prisoner by their smugglers. Official sources, who have requested not to be named, say the smugglers may be telling people they can only accept landing rights in Malaysia as the smugglers are possibly Thai and wish to avoid what has become a very high-profile issue.

Thailand will host a regional conference on May 29, where the issue will be high up on the agenda.

More immediately, Malaysia will play host to three-way meetings Wednesday between the foreign ministers of Indonesia, Malaysia and Thailand. Despite its pivotal role in the crisis, the Myanmar government will not send a representative.

Meanwhile, the U.S. has said that while the humanitarian disaster at sea is the most pressing concern, a State Department official tells CNN the fundamental issue lies in Myanmar.

Assistant Secretary of State for Democracy, Human Rights and Labor, Tom Malinowski, told CNN's Hala Gorani that the U.S. has offered assistance and is urging the governments of Thailand, Malaysia and Indonesia to work together to conduct search and rescue missions, and to allow the refugees to land.

"Our first responsibility is to save lives and that is something that has to be done in the coming days and hours. In the longer run, the biggest challenge is to get at the root cause of this crisis, the treatment of the Rohingya population inside Myanmar."

Myanmar

JUST WATCHED Rohingya migrants fleeing Myanmar Replay More Videos ... MUST WATCH Rohingya migrants fleeing Myanmar 02:36

Myanmar, also known as Burma, is home to a large Rohingya population, particularly in Rakhine state, in the west of the country.

Clashes in 2012 between the state's Buddhist community and Rohingya Muslims, a long-oppressed linguistic and ethnic minority in this majority Buddhist country, left hundreds dead and more than 140,000 people homeless.

The United Nations estimates more than 100,000 Rohingya have fled Myanmar by sea since ethnic and sectarian violence erupted.

The government has forcibly segregated Rohingya from the rest of the population in Rakhine state. They live confined in enclaves -- rural ghettos, in effect -- from which they are not allowed to leave. The government refuses to recognize them as a legitimate ethnic group and as citizens of Myanmar.

Those who have the means to leave do so by perilous sea journey. They are taken out on small boats to cargo ships by smugglers, mostly bound for Malaysia.

The government has said it will not participate in Thailand's regional conference on May 29. Zaw Htay, a director in the office of Myanmar President Thein Sein, told CNN: "We will not participate in the discussions next week if the name 'Rohingya' is mentioned.

"If we recognize the name, then they will think they are citizens of Myanmar... Myanmar cannot take all the blame for these people who are now at sea. We need long term (solutions) and you can't just explain it by saying Myanmar is the source of the problem. A long term solution is needed."

A statement from the Ministry of Foreign Affairs, published in state media on May 19, points to illegal smuggling as the root cause of the problem, and says that the Burmese government "shares concerns expressed by the international community," and that it is "fully prepared to work with the international community, on humanitarian grounds, to alleviate the sufferings of the smuggled victims." The statement makes no mention or acknowledgment of Rohingya claims to citizenship.

Bangladesh

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Between 7,000 (official figure) and 300,000 (U.N. estimate) Rohingya migrants live in neighboring Bangladesh, many in U.N.-operated or illegal camps on the other side of the Bangladeshi-Myanmar border, but they are unable to work in the country and live in deplorable conditions

The plight of the Rohingya currently abandoned at sea is exacerbated by the presence of Bangladeshi economic migrants in their midst. While many, including the UNHCR, see the Rohingya as legitimate refugees fleeing persecution, the Southeast Asian nations refusing to allow the ships cite the presence of economic migrants as a reason to refuse them refuge.

Matthew Smith of Fortify Rights , a non-profit human rights organization based in Southeast Asia, says Southeast Asian governments have the wherewithal to track and find them, but simply don't want to.

"Governments in the region are playing human ping-pong, pushing boats back out to sea while claiming to crackdown on human trafficking," he said . "All governments have a responsibility to protect survivors of trafficking and asylum seekers. No government can credibly claim to be combating trafficking while simultaneously creating a ready pool of desperate and insecure people at sea."

Malaysia

Charles Santiago, a Malaysian politician and chairman of the ASEAN Parliamentarians for Human Rights, said regional countries, as well as the U.S. and China, must push Myanmar to help the Rohingya.

"ASEAN promotes itself as an organization that promotes rule of law, democracy, a sharing and caring society... this is really a challenge, whereby the most vulnerable community in the region is now seeking help. And this isn't just any kind of help, this is a matter of life and death."

He said that the meetings in Malaysia and Thailand this week and next will be more about short-term solutions to the immediate crisis. In the longer term, he says that the regional governments have a role to play.

"The long-term solution is for ASEAN to put pressure on the Myanmar government to (implement) political reforms and make sure citizenship (for the Rohingya) is given."

Previously, however, a top Malaysian official had told CNN the surge of migrants from Myanmar and Bangladesh seeking asylum in his country and neighboring Indonesia in recent days is unwelcome -- and despite a U.N. appeal, his government will turn back any illegal arrivals.

"We cannot welcome them here," Malaysian Deputy Home Minister Wan Junaidi Jaafar said last week.

"If we continue to welcome them, then hundreds of thousands will come from Myanmar and Bangladesh."

Malaysia is hosting a meeting to discuss the issue in Kuala Lumpur on Wednesday, which will be attended by its foreign minister as well as those from Thailand and Indonesia.

"Malaysia remains committed to working closely with the affected countries and members of the international community in resolving this issue in the region. Malaysia will continue to seek a solution on this issue through, inter alia, concerted and coordinated efforts among the countries of origin, transit and destination."

Thailand

JUST WATCHED Rohingya migrant boat missing in the Andaman Sea Replay More Videos ... MUST WATCH Rohingya migrant boat missing in the Andaman Sea 02:32

In the Andaman Sea, aboard a fishing vessel searching Thai waters for vessels carrying refugees, a CNN crew saw several Thai navy vessels on patrol.

Kraiwut Chusakul, a local fisherman, said he's seen one of the many boats filled with Rohingya refugees. "There are so many children on the boat," he said. "I think there must have been around 100 small children."

The boat Kraiwut saw hasn't been seen since, and despite searching and asking other fishing boats if any refugee ships had been spotted, the CNN crew also turned up a blank.

"I feel so sorry for them," Kraiwut said. "It's so different to when you see these refugees on land, and the conditions are so terrible."

Late last week, residents on Koh Lipe Island in southern Thailand could be seen collecting food, water and clothes to take to the migrants on board the boats, but since then the military has told them not to take supplies out to the boats, or to talk to journalists about the situation.

Fortify told CNN that patrol ships stay ahead of those searching for these ships, chasing them out of territorial waters, so journalists and rights groups cannot get a clear understanding of the situation.

The country will host trilateral talks between the foreign ministers of Indonesia, Malaysia and Thailand this week in an attempt to resolve the current impasse, and will again host a larger meeting of ASEAN nations on May 29.

Indonesia

Indonesian military spokesman Fuad Basya told CNN on May 18: "We have four navy vessels guarding our territorial waters in Aceh now. The policy remains -- we won't let any illegal migrants in."

Its foreign minister, Retno Marsudi, will attend meetings in Kuala Lumpur Wednesday in an attempt to find a solution to the growing humanitarian crisis.

However, she told reporters Tuesday that Indonesia has "given more than it should" to help those stranded at sea.

The UNHCR reports that, in the last week, Indonesian fishermen have rescued more than 1,300 Bangladeshis and Rohingya, whose vessels had entered Indonesian territorial waters after they drifted or swam to shore in Aceh and North Sumatran provinces.

The chief of the Aceh Search and Rescue Agency (SAR), Budiawan tells CNN approximately 100 migrants were rescued Wednesday by fishermen and the SAR.

However, Indonesian fishermen were being discouraged from actively searching for and rescuing stranded refugees.

"If they encounter any boats then of course they can rescue and tow them in, for humanitarian reasons. But their job is to catch fish and they shouldn't be going out to search for these boats," Basya said.

The Philippines

Despite being geographically distant from the epicenter of this growing humanitarian crisis, the Philippines has offered to allow the migrant boats landing rights.

The government quickly reacted to a report in local press saying that it would "push back to sea" any refugees that tried to land on Filipino soil.

Herminio Coloma Jr., a spokesperson for the country's Presidential Communications Operations Office said in a statement May 18 that the Philippines has extended humanitarian assistance for "boat people" in the past, citing its establishment of a processing center for Vietnamese migrants in the 1970s.

Citing the 1951 Convention Relating to the Status of Refugees, or which the Philippines is a signatory, Coloma said: "We shall continue to do our share in saving lives under existing and long-standing mechanisms pursuant to our commitments under the Convention."