More than 620,000 people have poured into Bangladesh since August, running from a Myanmar military crackdown that Washington said this week clearly constitutes "ethnic cleansing against the Rohingya."
The talks between Suu Kyi and her Bangladeshi counterpart come ahead of a highly-anticipated visit to both nations from Pope Francis, who has been outspoken about his sympathy for the plight of the Rohingya.
Mainly Buddhist Myanmar, which denies committing atrocities against the Muslim minority, has agreed to work with Bangladesh to repatriate some of the Rohingya piling into desperately overstretched refugee camps.
But the neighbours have struggled to settle on the details, including how many Rohingya will be allowed back in violence-scorched Rakhine, where hundreds of villages have been levelled.
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Last week Min Aung Hlaing said it was "impossible to accept the number of persons proposed by Bangladesh".
"They discussed about the development of cooperation and relations between two countries, to accept the people who left the places of Rakhine, and ongoing cooperation between two countries," Myanmar's Ministry of Foreign Affairs said in a statement.
Officials could not be reached for comment about whether a final deal was on the cards.
The stateless Rohingya have been the target of communal violence and vicious anti-Muslim sentiment in mainly Buddhist Myanmar for years.
The latest crisis erupted after Rohingya rebels attacked police posts on August 25.
The army backlash rained violence across northern Rakhine, with refugees recounting nightmarish scenes of soldiers and Buddhist mobs slaughtering villagers and burning down entire communities.