Police or Border Guard Bangladesh however, could not confirm the numbers.
The Rohingya are not formally recognized as citizens - the Myanmar government does not even use the term Rohingya, referring to the group as "illegal immigrants" from neighboring Bangladesh, a Muslim-majority country.
"Under the principle of non-refoulement, countries are under obligation not to send back refugees to their country of origin where circumstances of grave human rights violations prevail", CHRI's Director Sanjoy Hazarika said in the statement.
The UN believes those security "clearances" may have amounted to ethnic cleansing of the Rohingya, a mainly Muslim minority living in Buddhist Myanmar.
"Sad news has reached us of the persecution of our Rohingya brothers and sisters, a religious minority", the pope said to pilgrims and tourists in St. Peter's Square.
Thousands of people have fled their homes following two days of violence in a deepening crisis in the state of Rakhine in Myanmar. "All 90 were detained and later pushed back to Myanmar by the border guards." local police chief Abul Khaer said, adding that the refugees were on their way to a camp in Kutupalong, where thousands of Rohingyas already live.
The spat, which is the worst since last October, has prompted the government to evacuate staff and non-Muslims from the area.
A local public representative confirmed that 2,000 Rohingyas entered Bangladesh through different points of Naikhyangchhari.
But a previously unknown militant group emerged as a force in October 2016 under the banner of the Arakan Rohingya Salvation Army (ARSA), which claims to be leading an insurgency based in the remote May Yu mountain range bordering Bangladesh.
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"They fired so close that I can not hear anything now", Mohammad Zafar, 70, said of armed Buddhists who had shot dead his two sons in a field.
"She's been shockingly irresponsible with this crisis", he said.
"We grew up with them".
"I would like to express my full closeness to them".
Civilians in northern Rakhine have since been trapped between security forces and the militants - who are accused of conducting a shadowy assassination campaign against perceived collaborators with the state.
Clashes continued on Sunday, with witnesses in the northern Rakhine town of Maungdaw saying they could hear gunshots.
Rights group asks Bangladesh not to turn away refugees, and slams Aung San Suu Kyi's "unacceptable response" to crisis.
Suu Kyi's government has hit out at some worldwide agencies since the fighting began a year ago in Rakhine.
"They arrest and beat whoever they see along the way", a man, who gave his first name as Anawar, told AFP Sunday morning by phone. "We want a peaceful and calm society".