She led the populist National League for Democracy (NLD) to win Myanmar's first open election in 25 years in November 2015 that led to the military relinquishing control of the country.
"Together both countries will ensure that terror is not allowed to take roots in our country", de-facto leader Aung San Suu Kyi said.
But in her Nobel lecture in 1991, Ms Suu Kyi said: "Wherever suffering is ignored, there will be the seeds of conflict, for suffering degrades and embitters and enrages".
"My dear sister: If the political price of your ascension to the highest office in Myanmar is your silence, the price is surely too steep ..."
Mr Tutu said that he had come out of retirement to make the comments because he was so deeply moved by the situation.
"We know very well, more than most, what it means to be deprived of human rights and democratic protection". A country that is not at peace with itself, that fails to acknowledge and protect the dignity and worth of all its people, is not a free country'.
"It is not possible to strip a Nobel Peace Prize laureate of his or her award once bestowed", Njolstad wrote.
Ms Suu Kyi, feted for her years of peaceful opposition to Myanmar's junta rulers, has been urged to speak up for the Rohingya, with Muslim nations and the UN leading the condemnation of her government.
However, the organisation that oversees the coveted prize has said the honour can not be withdrawn.
A Rohingya Muslim whom the Associated Press reached by phone said that she and thousands of fellow villagers driven from their homes by the violence in Burma are now stuck along the coast, hoping to flee to nearby Bangladesh by boat.
Despite evidence that the crimes have been committed by the Burmese military, Ms Suu Kyi has blamed the violence on "terrorists" and claimed the controversy has been caused by "a huge iceberg of misinformation". It goes back to pre-colonial times, ' she added.
"It is a little unreasonable to expect us to solve the issue in 18 months", she told the Delhi-based network Asian News International.
"The Rohingya fleeing Myanmar are now stateless refugees, making them even more vulnerable and adding more challenges to the search for solutions".
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