US Deputy Assistant Secretary of State Patrick Murphy is expected to travel to Myanmar in the coming days for discussions on the crisis, after summoning Myanmar's ambassador to express US concerns on Wednesday.
He also called the violence, which has disproportionately affected the country's Rohingya Muslim community, "unacceptable", and said the attacks - which some have deemed ethnic cleansing - "has to stop".
Almost three weeks into a mass exodus of Rohingya Muslims fleeing violence in Myanmar, thousands are still flooding across the border in search of help and safety in teeming refugee settlements in Bangladesh.
In a letter addressed directly to the Burmese leader seen by the Daily Telegraph, Ms Thompson wrote: "Few people have inspired me in my life the way you do. but I can not stay silent when women and children suffer".
Muslim militants in Burma have insisted that they have no connection with jihadists after claims that the ethnic cleansing of the Rohingya could incite Islamist terrorism.
"I think nobody wants to see a return to military rule in (Myanmar), nobody wants to see a return of the generals", he said, adding that Nobel Peace Prize laureate Suu Kyi should use her moral capital to highlight the plight of the Rohingya.More news: Trump heads to Florida to survey damage from Hurricane Irma
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"I think it is important that the global community speak out in support of what we all know the expectation is towards the treatment of people, regardless of their ethnicity, and that we must? this violence must stop; this persecution must stop".
Thant Myo Htway, one of the protestors, said "We strongly condemn the actions of ARSA Bengali extremist terrorists that damages our nation's sovereignty".
Violence in Myanmar has invited reactions from around the world.
Aung San Suu Kyi will give a public address next week on the crisis involving Burma's Rohingya minority, her spokesman has said.
The refugees are fleeing a fresh security operation in which security forces and Buddhist mobs have killed men, women and children, looted homes, and torched Rohingya villages.