Michael Dwyer was one of three people killed last week by Bolivian police who the leftist government said belonged to a gang of "famous mercenaries" who were planning to assassinate Morales.
Irish Foreign Minister Micheal Martin said Dwyer had no criminal record or army background in Ireland.
"The Irish Government has a legitimate right to seek the facts of how one of its citizens came to be killed by the security forces of another state," Martin said in a statement.
Bolivian officials have named the group's "ringleader" as Eduardo Rozsa, a Bolivian who may have also held Hungarian and Croatian passports, and who fought in separatist movements during the Balkan wars.
A Romanian citizen was also killed in the incident.
"Prima facie evidence is sufficient to raise questions in relation to the description of events released by the Bolivian authorities," Martin said.
He also said Dwyer had been identified and "gruesome" footage of his dead body displayed in international media before contact had been made with Irish diplomats.
"I want to make it clear that Ireland had no involvement in or has no sympathy for any action designed to destabilise Bolivia or threaten the security of its democratically elected president," he said.
Leaders of Bolivia's rightist opposition on Tuesday condemned the shootings which took place in the eastern city of Santa Cruz, an opposition stronghold, as police moved to arrest the group.
Morales, who accused rivals in Santa Cruz of organising violent protests last year, has linked the suspected plot to right-wing opponents he says are seeking to destabilise his government. The opposition denied any links to the alleged plot.
