According to Brazilian media reports, the incident began as suspected smugglers who were trying to enter Brazil through the Parana river, opened fire on Brazilian troops.
On Sunday, Paraguayan Foreign Minister Eladio Loizaga accused and criticized Brazilian troops for crossing into Paraguayan territory during the shoot out.
Loizaga went on to demand an apology and a “satisfactory explanation” regarding last month’s confrontation.
According to Brazilian State news agency, the Brazilian government is investigating the incident and will issue an official response for the Paraguayan government by Monday.
Last July, the Brazilian Armed Forces deployed 4,200 soldiers along Brazil's western border with Paraguay and Bolivia in order to curb trans-border crimes such as smuggling, drug and human trafficking, and illegal mining.
Brazil notified Paraguay and Bolivia of the military operation and both sent official representatives to observe the actions from Campo Grande, the capital city of Mato Grosso do Sul.