The United States said Myanmar's government should treat minority Rohingya Muslims as citizens to solve the root cause of the migrant crisis in Southeast Asia, and called on Wednesday on all Myanmar's leaders to speak up on human rights issues.

US President Barack Obama has sought to make Myanmar's transition to democracy a legacy of his presidency, and Washington is stepping up pressure on the country to tackle what it sees as the underlying causes of an exodus of "boat people" across the Bay of Bengal that the region has struggled to cope with.

Many of the more than 4,000 migrants who have landed in Indonesia, Malaysia, Thailand and Myanmar since the Thai government launched a crackdown on people-smuggling gangs are Rohingya who say they are escaping persecution.

Myanmar does not recognise its 1.1 million-strong Rohingya minority as citizens, rendering them effectively stateless. Many have fled the apartheid-like conditions of the country's Rakhine state. Myanmar denies it discriminates against them.

"Rohingyas need to be treated as citizens of Burma," US Assistant Secretary of State Anne Richard told reporters at a press briefing in Jakarta, using the country's former name.

"They need to have identity cards and passports that make clear they are as much citizens of Burma as anyone else."

Obama said on Monday that Myanmar needed to end discrimination against the Rohingya people if it wanted to succeed in its transition to a democracy.

Politicians in Myanmar were focused on a historic general election scheduled for November, Richard said, which was hindering political discussion of the status of the Rohingya.

Images of desperate people crammed aboard overloaded boats with little food or water has focused international attention on the region's latest migrant crisis, which blew up last month after the Thai crackdown made it too risky for people smugglers to land their human cargo, who were instead abandoned at sea.