In an interview with Radio Free Asia, the UN envoy said he is currently looking into the details of the deadly incident in Pegu township last weekend, describing the killings as a violation of human rights.
The funerals of the two young men, Aung Thu Hein, 22, and Soe Paing Zaw, 18, were held in a tense atmosphere on Tuesday. They were shot dead by soldiers from the Southern Command's Infantry Battalion 59 on Saturday after a dispute between them and officers from the battalion near a local restaurant.
Family members said they have no hope of legal recourse over the deaths of their loved ones.
“How can we rely on the legal system? We can't even file this case at the police station,” said Aung Thu Hein's aunt.
No one except close family members was allowed to see the corpses before they were cremated, and security was tight all over the town during the funeral.
“Plainclothes security officials were everywhere. They questioned us about how we were related to the victims before allowing us to see their bodies,” she said.
According to locals, the family of one of the victims accepted the army's offer of one million kyat (US $1,000) in compensation, but the other family has not.
Several candidates of political parties contesting in the November election as well as members of the National League for Democracy, which is boycotting the polls, attended the funeral to show solidarity with the victims' families.
“This incident shows us that this lawless government can do whatever it wants with impunity. This is a threat to the public which will last until election day,” said Thein Htay, the leader of the Union of Democracy Party, who attended the funeral.
“I was photographed once and checked three times on my way from Rangoon to Pegu for the funeral,” he said.
Quintana has recently recommended that the UN establish a Commission of Inquiry into war crimes and crimes against humanity by the Burmese government. The idea has increasingly received the support of a number of countries including the United States.