The United Nations refugee agency wants an investigation into the death of two Iraqis who were reportedly severely beaten by Bulgarian border guards and died of hypothermia while trying to cross from Turkey.

The statement on Tuesday says the two men were likely refugees from the Yazidi religious minority group. It calls on both Turkey and Bulgaria to investigate and says, "It is deeply disturbing that people in search of international protection are being turned away, often with violence."

The EU agency that tracks the flow of illegal immigration along smuggling routes, Frontex, has said numbers along that route are soaring because Turkey currently hosts more than 1 million refugees from Syria, Iraq and Afghanistan.

The UNHCR statement says a third Iraqi man in the incident was left in critical condition.