Rights groups have criticised the announcement as a publicity stunt and Bangladesh has distanced itself, saying the repatriation was not part of the return process the two countries have been trying to start.
In an effort to address the crisis, Bangladesh and Burma signed a deal in November to repatriate the Rohingya over the course of two years, beginning in January. The United States government and the United Nations describe the violence against the Rohingya as "ethnic cleansing".
The UN chief said the assaults were allegedly perpetrated by the Myanmar Armed Forces, known as the Tatmadaw, "at times acting in concert with local militias, in the course of military "clearance" operations in October 2016 and August 2017". Myanmar set up two reception centres and what it says is a temporary camp near the border in Rakhine to receive the first arrivals.
The family members were scrutinized by immigration and health ministry officials and the social welfare, relief and resettlement ministry provided them with "materials such as rice, mosquito netting, blankets, t-shirt, longyis (Burmese sarong) and kitchen utensils", said the government in the statement.
It is being said, the family members were issued National Verification Cards (NVCs) upon entering Myanmar.
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Rights groups are expressing scepticism over the announcement that Myanmar has repatriated the first Rohingya family, despite warnings from the UN.
No further information has been given about other possible repatriations.
Myanmar has denied almost all allegations, saying it waged a legitimate counter-insurgency operation.
Andrea Giorgetta from the International Federation for Human Rights (FIDH) criticised the repatriation announcement as "a public relations exercise in an attempt to deflect attention from the need for accountability for crimes committed in Rakhine state".
They have been systematically stripped of their citizenship in recent decades and forced to live in apartheid-like conditions with severely restricted access to health care, education and other basic services. The card has been widely rejected by Rohingya community leaders, who say they treat life-long residents like new immigrants. The latest confirmed departure took place on Thursday.