Boris Johnson has warned Aung San Suu Kyi that the treatment of the Muslim Rohingya people is "besmirching the reputation" of Burma.
Tens of thousands of people have fled into Bangladesh in an effort to escape the violence in western Burma, according to the UN's refugee agency.
Burmese security officials and insurgents from the Rohingya are accusing each other of burning down villages and committing atrocities in Rakhine state.
Almost 400 people have died in the recent outbreak of violence.
In a message to the country's de facto leader Ms Suu Kyi, who won the Nobel Peace Prize for her pro-democracy activism, the Foreign Secretary urged her to use "all her remarkable qualities" to end the violence.
He said: "Aung San Suu Kyi is rightly regarded as one of the most inspiring figures of our age but the treatment of the Rohingya is alas besmirching the reputation of Burma.
"She faces huge challenges in modernising her country. I hope she can now use all her remarkable qualities to unite her country, to stop the violence and to end the prejudice that afflicts both Muslims and other communities in Rakhine.
"It is vital that she receives the support of the Burmese military, and that her attempts at peacemaking are not frustrated. She and all in Burma will have our full support in this."