Diplomats say Myanmar has up to now resisted calls for it to take part in meetings on the stranded "boat people", 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.
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.
"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 Reuters 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.
"We will continue to encourage Myanmar in their process of reform and democratization. Because in the end we believe it will create an environment conducive for the Rohingya," said Armanatha Nasir, a spokesman for Indonesia's foreign ministry.
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.
Indonesia and Malaysia have said that temporary shelters would be set up to house the migrants but Thailand, a traditional transit point for migrants trying to reach Malaysia illegally to find work, said it would not follow suit.
"There will definitely be no migrant shelters," Thai Prime Minister and coup leader 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.
Thailand has said it would stop towing boats back to sea, something Malaysia and Indonesia had been doing in recent days, and will allow the sick to come to shore for attention, but has stopped short of saying whether it would allow other migrants to disembark.
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