"The talks were held in a friendly atmosphere, and Myanmar has made a proposal to take back the Rohingya refugees", Mahmood said after the meeting in Dhaka.
There were already about 300,000 Rohingya refugees in Bangladesh before the most recent exodus.
The Bangladesh minister gave no time frame for repatriation.
"We have also agreed on forming a joint working group to oversee the repatriation process", Ali said adding that Bangladesh had also handed draft of a bi-lateral agreement to Myanmar for the possible repatriation process.
Nobel peace laureate Suu Kyi, who has been severely criticised for her failure to curb the military crackdown on the Rohingya, said in a speech last month that Myanmar would take back "verified" refugees.
While talking about Myanmar's attitude towards repatriation, the minister said: "If we comment or express any doubt regarding that matter then discussion process might be delayed".More news: Benjamin Mendy's season in doubt after confirmation of ACL injury
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Under global pressure, Aung San Suu Kyi, in her speech last month, had spoken of taking back the Rohingyas, but had said Myanmar would conduct a process of verification.
They are accused of being among dozens of protesters from Sri Lanka's majority Buddhist community, including monks, who stormed a safe house on the outskirts of Colombo where 31 Rohingya Muslims who fled Myanmar, including 17 children, had been living since arriving in the country in April.
Home Minister R. Lalzirliana on Sunday said that the State government has not received any report of even a single Rohingya entering its soil till date.
Myanmar told the United Nations refugee agency on Monday that its top priority was to bring back Rohingyas who have fled to Bangladesh. Ever since the latest flare-up of violence against the community in Myanmar this year, almost 4 lakh Rohingyas have fled the state, pouring into nearby countries like Bangladesh seeking refuge.
The head of the United Nations' food-assistance agency on Sunday urged the worldwide community to step up its support for the relief operation for Rohingya refugees in Bangladesh or risk "a massive catastrophic disaster".
The Indian envoy said Myanmar security forces' operations resulted in the exodus of a large number of people from Rakhine State, many of whom have sought shelter in neighbouring Bangladesh.