Niki Lauda apologised personally to Robert Kubica in Monaco last weekend.
Former triple world champion Lauda, whose straight-talking assessments are still heard at every Grand Prix, referred to the Renault driver live on German television as "der Polack" (the Polack).
Polack is a derogatory reference to a Polish person, and even more offensive within Germany given the 1939 Nazi invasion that marked the start of World War II.
Germany's Auto Motor und Sport said officials of the German TV station RTL demanded that Lauda, 60, apologise.
"I have to say to Robert that it was meant in a nice way," said the Austrian. "I was just happy that he drove his car onto the front row."
Lauda reportedly waited for 15 minutes at the Renault motor home on Sunday morning and did apologise publicly to the 25-year-old.