The Dalai Lama has urged Aung San Suu Kyi to find a peaceful solution to the crisis in Myanmar and expressed concerns about violence that has led around 300,000 Muslim Rohingya to flee the Buddhist-majority country.

The top Buddhist leader wrote to Myanmar's de facto civilian leader, a fellow Nobel peace laureate, shortly after new violence erupted in Rakhine state in August.

He urged her to "reach out to all sections of society" to try to resolve the crisis in Rakhine, where the Rohingya, a stateless Muslim minority, have endured decades of persecution.

"Questions that are put to me suggest that many people have difficulty reconciling what appears to be happening to Muslims there with Myanmar’s reputation as a Buddhist country," he wrote in the letter, seen by AFP on Monday.

"I appeal to you and your fellow leaders to reach out to all sections of society to try to restore friendly relations throughout the population in a spirit of peace and reconciliation."

The Dalai Lama is the latest Nobel peace laureate to speak out against the violence, which the UN special rapporteur on human rights in Myanmar says may have left more than 1,000 dead, most of them Rohingya.

Nobel laureates Malala Yousafzai and Archbishop Desmond Tutu have also urged her to intervene on behalf of the Rohingya.

"If the political price of your ascension to the highest office in Myanmar is your silence, the price is surely too steep," said Tutu, who became the moral voice of South Africa after helping dismantle apartheid there.

Myanmar's population is overwhelmingly Buddhist and there is widespread hostility toward the Rohingya, who are denied citizenship and labelled illegal "Bengali" immigrants.

Buddhist nationalists, led by firebrand monks, have operated a Islamophobic campaign calling for them to be pushed out of the country. 

The Dalai Lama said he had spoken to Suu Kyi in the past about religious tensions in her country and was urging her again to curb the violence.

"As a fellow Buddhist and Nobel laureate I am appealing to you and your colleagues once more to find a lasting and humane solution to this festering problem," he wrote.