"We are denouncing to the country and to the world that behind this assassination attempt there is a plot, a sinister plan whose reach we still don't know. But we are aware of the motives," said Juan Ramon Quintana, the cabinet chief of staff.
Willians Torres, a local prosecutor, said the men were arrested in the city of Santa Cruz itself, not at the airport.
"It's not a crime to carry guns," Torres told AP news agency by telephone.
"There was no reason to keep them detained, but the investigations will continue."
The interior ministry, in charge of security, said the two men were members of a conservative Santa Cruz youth group that has led protests against Morales' policies.
The group itself denied that the two were members.
Many in Santa Cruz, the country's wealthiest province, oppose Morales's policies, which include redistributing land to the poor and overhauling the nation's constitution.
The eastern region's conservative leaders are waging a campaign for greater autonomy from the central government.
Last month, Santa Cruz residents voted in a referendum for the regional government to take greater control over local legal and economic affairs.