In a letter sent to FIFA after the game, Colombia's Soccer Federation said the hostility of the Brazilian federal police team assigned to them was causing discomfort among players and technical staff.
"They have torpedoed Colombia's movements, taking the team at a very slow speed," team spokesman Mauricio Correa told Reuters.
"Because of this situation yesterday we were late for the match ... It was intentional."
Despite the problems, Colombia had no trouble overpowering Greece 3-0 at the Mineirao stadium in Belo Horizonte.
Back in Sao Paulo, where the team are based for the tournament, new rifts erupted with the security detail.
"There were not so kind words on their part and some members of our delegation were pushed over," Correa said, stressing no players were involved in the incident.
He said that after complaining to FIFA their security team had been replaced and things were now back to normal.
In a statement issued later on Sunday, Brazil's Justice Ministry, responsible for the security of the visiting teams, said it had addressed Colombia's concerns.
"All possible measures were already taken to guarantee the security of the Colombian team in all its movements around the country," the Ministry said.
Colombia face Ivory Coast on Thursday in Brasilia. Their last Group C game is on June 24 against Japan.
(Reporting by Esteban Israel, editing by Ed Osmond)
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