The incidents took place during NATO's "Trident Javelin" exercise in the southern Norwegian city of Stavanger aimed at increasing coordination between the allies at headquarters level, which wound up Friday.
While media reports have suggested that a technician and an officer, responsible for the incident were fired, NATO Secretary General Jens Stoltenberg refuted this saying that the responsible individual was not an employee of NATO.
In a second incident, a chat account was opened under Erdogan's name during a virtual scenario as a collaborator with a "leader of an enemy state".
The Joint Warfare Center, which conducts the drills, is a multinational North Atlantic Treaty Organisation unit some 200 kilometers southwest of Oslo. "There are some mistakes that are done not by fools but only by base people", Erdogan said in an event in northeastern Rize.
"This matter can not be covered over with a simple apology", he added.
Turkey's candidacy for membership of the European Union has also effectively stalled, and the union was critical of President Erdogan's crackdown on academia and the judiciary following an attempted military coup past year.
A portrait of Turkey's founder Mustafa Kemal Ataturk was also shown in the "hostile leader list" during a computer-assisted exercise.
Turkey withdrew all 40 of its participating troops in response.
Speaking at an event in Ankara on Saturday, the Republican People's Party (CHP) leader Kemal Kilicdaroglu said they can not accept the "insult" towards Turkey's history and current executives.
The contractor was removed from the exercise and an investigation is underway, he said.
"I apologize for the offense that has been caused", Stoltenberg said. "We strongly condemn this". They said they had made a decision to withdraw the soldiers.
Erdogan said that Ankara had withdrawn its 40 troops from the exercise in protest, adding: "It's not possible to have this kind of alliance".