The violence was triggered after a Buddhist man posted a photo of a burning Koran on the social network site Facebook.
Dr Pornchai Pinyapong, head of the World Fellowship of Buddhist Youth, said the group came out to denounce the violence in Chittagong, Bangladesh which injured several Buddhists, including a monk.
Its petition asks the UN and the government to pressure Bangladesh into protecting Buddhists. They also want the damaged temples repaired.
A UN representative, and Leelawadee Watcharobol, of the Senate committee on religion, arts and culture, received the petition.
The group also handed its demand to the embassy of Bangladesh in Bangkok on Tuesday.
"We are monitoring the news closely and if the violence shows no sign of stopping, we will pressure the government to stop issuing visas for Muslim Bangladeshi citizens," Dr Pornchai said.