Ties between the neighbours have been severely strained by army-led violence in Myanmar's Rakhine state that has driven more than 600,000 Rohingya into Bangladesh since late August.
The exodus has saddled one of Asia's poorest nations with a massive humanitarian crisis, with refugees too terrified to return to Rakhine.
Dhaka and the UN have accused Myanmar's army of ethnic cleansing and called for the full repatriation of the Muslim minority, who have crammed into makeshift camps in Bangladesh's Cox's Bazar district.
After talks in Myanmar's capital Naypyidaw yesterday, Bangladesh's Home Ministry said Myanmar had agreed to stop the outflow of Rohingya and take back all refugees.
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"Myanmar has agreed to stop continuous entry of displaced Myanmar nationals in Bangladesh and to bring normalcy back to the Rakhine State," the Home Ministry said in a statement.
But Myanmar offered a more measured commitment, saying only that refugees would need to be scrutinised for proof of their roots in Rakhine state.
"We cannot say when we are going to receive (the refugees)," Tin Myint, from Myanmar's Home Ministry, told reporters after the meeting.
That criteria may be difficult to fulfil for the Rohingya who bolted from Myanmar soldiers and Buddhist mobs who they allege drove them out with a massive campaign of arson, murder and rape.
Also, Myanmar has rendered the Rohingya stateless with the government refusing to recognise them as a distinct ethnic group.
Myanmar has vehemently rejected accusations of ethnic cleansing and defended the army campaign as a legitimate response to August 25 attacks by Rohingya militants.
Even if the reparation plan goes forward, there is widespread concern over what the Rohingya will return to, since many of their villages have been razed by fires.