Malaysia has sent four navy ships to look for stranded migrants at sea, while a Thai official has said Myanmar has agreed to attend an emergency conference on the crisis.
The Malaysian and Indonesian navy chiefs have been discussing ways to coordinate search and rescue efforts.
Earlier on Thursday, Malaysia's Prime Minister Najib Razak ordered the navy to take action to rescue the estimated thousands of migrants adrift on boats.
Malaysia and Indonesia say they will temporarily house migrants who land on their shores.
But Thailand, which is a major transit point for the migrants, says it will not shelter them.
"There will definitely be no migrant shelters," Thai Prime Minister Prayuth Chan-ocha told parliament in Bangkok on Wednesday, adding that existing detention centres would be used to hold those found to have entered Thailand illegally.
Diplomats say Myanmar had up to now resisted calls for it to take part in meetings on the stranded refugees, many of them Rohingya Muslims who have long complained of discrimination in Myanmar.
The apparent shift in its position came after Malaysia and Indonesia's foreign ministers held talks with senior officials in Myanmar on Thursday.
Western powers and aid groups have also urged Myanmar to increase its involvement, and called on regional powers to do more.
US Deputy Secretary of State Antony Blinken also held meetings in Myanmar on Thursday, seeing its president, foreign minister, parliamentary speaker and military commander.
Blinken stressed the need for Myanmar to address the root causes of the migration, "including the racially and religiously motivated discrimination and violence," State Department spokeswoman Marie Harf told a news briefing.
The crisis has seen thousands of migrants, also including Bangladeshis fleeing persecution and poverty at home, pushed back out to sea by Thailand, Malaysia and Indonesia.
Many now face sickness, and possible starvation, say aid groups.
"I have further ordered @tldm_rasmi (navy} and APMM (Malaysian Maritime Enforcement Agency) to conduct search and rescue efforts on Rohingya boats," Najib said on his Twitter account on Thursday.
"We have to prevent loss of life," he said, adding that humanitarian aid would be delivered by land and sea.
Malaysia and Indonesia on Wednesday said they would let as many as 7,000 migrants on the seas now to come ashore temporarily, but no more.
A Thai official told the Reuters news agency Myanmar had agreed to attend a regional summit on the issue in Bangkok next week, without going into further details.
Officials in Myanmar did not respond to requests for comment.
Rohingya Muslims have complained of state-sanctioned discrimination in majority-Buddhist Myanmar and are denied citizenship.
Myanmar denies discriminating against the group and has said it is not the source of the problem.
Thailand has said it will stop towing boats back to sea, something Malaysia and Indonesia had been doing in recent days.
It has also said it will allow the sick to come to shore for attention, but has stopped short of saying whether it will allow other migrants to disembark.