Mr. Marchionne, who is also head of Chrysler, said this week Volkswagen was being too aggressive in its pricing strategy when conditions are already tough in the European auto industry.
"Marchionne is unbearable as president of ACEA," Volkswagen communications chief Stephan Gruehsem said on Thursday. "In our view, his comments are unqualified yet again. We're therefore calling on him to step down."
Mr. Marchionne told The International Herald Tribune on Thursday the European auto market is the toughest he has ever experienced.
"It's a bloodbath of pricing and it's a bloodbath on margins," he said.
Mr. Marchionne again called for the European Commission to step in and help the industry confront the huge overcapacity problems, the paper said.
"What they should do is coordinate a rationalization of the industry across the producing companies," he said. "The ones that really have not acted on this are the French and the Germans, who have not taken out any capacity at all."
Volkswagen, Europe's largest automaker by sales, is considering quitting ACEA in protest over Marchionne's remarks.
The Wall Street Journal reported Volkswagen sales chief Christian Klingler dismissed Mr. Marchionne's pricing remarks during a conference call with analysts earlier on Thursday.
Mr. Klingler said VW isn't pursuing overly aggressive pricing in Europe. He noted, however, that competition in Europe is rising, the paper said.
The criticism highlights the tension between VW, which reported record first-half profit, and smaller European competitors such as Fiat of Italy and PSA Peugeot Citroen of France, whose losses in the region are mounting.
The European auto market faces an "elevated risk," as competition has increased "significantly," Mr. Klingler said today. Auto pricing in Europe is "tense" and "pressure" will continue in the coming months, he added.
Fiat and Volkswagen and have a history of sparring in public.
Volkswagen executives routinely express interest in purchasing Fiat's troubled Alfa Romeo brand despite Mr. Marchionne's refusal to divest the unit.
Volkswagen's influential supervisory board chairman, Ferdinand Piech, caused an uproar years ago when he told reporters that Fiat "isn't struggling enough yet" to be forced to sell Alfa Romeo.
On Thursday, VW posted higher second-quarter profits and reconfirmed its full-year target of flat earnings over 2011 despite large investments in new vehicles and intensifying price pressure in Western Europe, where new car sales have been declining for months.
New-car sales have been shrinking for months across Europe.
Analysts and industry executives expect the market to drop further in coming months with joblessness high and economic uncertainty mounting.
Several countries have adopted tough austerity measures to tackle a punishing sovereign-debt crisis.
Analysts estimate that the European auto industry is saddled by around 20% overcapacity. The glut weighs on earnings and makes it difficult for many automakers to operate profitably in the region.
Politicians and labor unions have vowed to resist large cutbacks.
But Peugeot, GM and other mass-market companies face mounting pressure to slash capacity.
Fiat's finances have benefited from its majority stake in Chrysler Group, which is generating profits again following its restructuring under Chapter 11 in 2009.
But new-car demand in Fiat's home market, Italy, has been plummeting because of the tough austerity measures.
-- Reuters, Bloomberg and David Phillips contributed to this Automotive News report.