The incident happened during a Nato military exercise in the southern Norwegian city of Stavanger and resulted in Ankara withdrawing its 40 troops last week.
In a telephone conversation with Erdogan on Saturday, Nato chief Jens Stoltenberg "reiterated his apology for the incidents" and said "that disciplinary action has been taken against the individual in question, and
that procedures are being put in place to prevent any such incident in the future," according to an alliance official.
In one incident an image of a statue of Ataturk had been used to portray an enemy protagonist in a scenario at the exercise, according to Turkey's foreign ministry.
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".
Stoltenberg had already apologised Friday to Turkey, which has Nato's second-largest army after that of the United States, after an angry response from Erdogan that risked deepening the rift between Ankara and its allies.
Stoltenberg told Erdogan on Saturday that he blamed "the actions on an individual" which do not reflect the views of NATO, adding that the person concerned was hired by the Norwegian army, not from within Nato.