The group refused to enter Bangladesh in the months during and after Myanmar's military campaign, which drove 700,000 other Rohingya across the frontier in an act the United Nations, United States and other western countries have condemned as ethnic cleansing.
They are now stuck in a narrow "no mans land" relying on international aid sent by Bangladesh.
Myanmar called for the aid to be halted in talks between Bangladeshi Foreign Minister A.H. Mahmood Ali and Myanmar's top diplomatic envoy, Kyaw Tint Swe, in Myanmar's capital Napyidaw on Friday, the foreign ministry said late Saturday.
"Myanmar particularly requested Bangladesh to stop providing humanitarian assistance to those people... and proposed to arrange supply of humanitarian assistance from Myanmar side," the ministry said.
Bangladesh made no commitment but "responded positively" to Myanmar's proposal to conduct a survey of the no mans land area, the ministry said.
A Myanmar minister on a visit to the strip of land earlier this year warned the Rohingya refugees that they will face "consequences" if they do not take up a Myanmar offer to return.
Dil Mohammad, a Rohingya community leader among the group on the border, told AFP the latest pressure from Myanmar to vacate the no mans land area would add to their hardship.
"There will be uncertainty whether Myanmar will regularly provide us with food and humanitarian assistance. If Bangladesh stops helping us from their side, we will have a huge problem," he said.
Kyaw Tint Swe, a minister in the office of Myanmar's de facto leader Aung San Suu Kyi, also made a new pledge to speed up implementation of a repatriation deal agreed with Bangladesh in November.
Myanmar committed to taking the Rohingya back in that deal, but none have returned. Rohingya leaders say that those sheltering at overflowing refugee camps in Bangladesh will not go back until their safety is guaranteed.
The majority of Myanmar's Rohingya fled the country following a crackdown that started last August after attacks by Rohingya militants on police posts.
They have joined about 300,000 in camps around Bangladesh's Cox's Bazar district who fled earlier waves of violence in Myanmar.
Myanmar views the Rohingya as illegal migrants and has long denied them citizenship and basic rights, despite their long roots in the country's west.