The two governments agreed to repatriate 2,251 of some 723,000 Rohingya refugees living in camps in Cox's Bazaar of Bangladesh.
Asean has mulled dispatching representatives to Myanmar to oversee the repatriation and resettlement of the refugees after Myanmar and Bangladesh reached an agreement at the end of October to send thousands of them back beginning today.
It also quoted other refugees as saying they were reluctant to go back and afraid of the military presence.
Rohingya activists have also lobbied against repatriation and even threatened foreign workers and camp elders who have suggested that the refugees should return.
"We are grateful to the Bangladesh government, the Bangladeshi people for their help".
U.S. Vice President Mike Pence expressed the Trump administration's strongest condemnation yet of Myanmar's treatment of Rohingya on Wednesday, telling leader Aung San Suu Kyi in Singapore that "persecution" by the Myanmar army was "without excuse".
The bilateral with Myanmar's leader Aung San Suu Kyi focused on the situation with the Rohingya, a spokesperson for the prime minister said. It said China, India and Japan were "providing necessary assistance" for the repatriation process, but did not give details.
Over 720,000 of Myanmar's stateless Rohingya fled in August past year, taking shelter in crowded camps in Bangladesh and bringing with them harrowing tales of rape, murder and arson in the brutal military crackdown.
In a meeting on the sidelines of a regional summit in Singapore, Pence told Suu Kyi that he was anxious to hear about progress in resolving the crisis, which stems from a violent military crackdown in Myanmar's Rakhine state that the United Nations has called ethnic cleansing.
Some 18,000 Rohingya women and girls were raped by Myanmar's army and police and over 115,000 Rohingya homes were burned down and 113,000 others vandalized, it added.
"I look forward to speaking with you about the premium that we place on a free and independent press", he said.
The military is in charge of security operations, including those in northern Rakhine.
More than 723,000 Rohingya have fled state-sponsored violence against their communities since August 2017.
They need equal rights, including citizenship, instead of restrictions that prevent them from finding work, attending school or seeing a doctor.
"Movement restrictions mean they can't travel freely, and as a result [they] struggle to access schools, hospitals and markets".
Many people who fled earlier violence and moved into displacement camps inside Myanmar have been unable to leave those settlements for years. Many in the Buddhist-majority country call the Rohingya "Bengalis", suggesting they belong in Bangladesh. Marked by their religion and their language - most speak a dialect of Bengali, while most of their neighbors speak Rakhine - they are easy to target.