The spat has highlighted growing tensions over fierce price competition in the slumping European car market.
A sparring match between the pair began with remarks Marchionne made in July about the German carmaker, which has been clawing business from smaller rivals in Europe.
Marchionne accused Volkswagen in a newspaper interview of being too aggressive and undercutting competitors.
In response, Volkswagen, whose European market share reached 25 percent in the January-August compared with 11.9 percent for number two PSA Peugeot Citroen (PEUP.PA), called for Marchionne to quit as president of the lobby group.
Marchionne's repeated calls for co-ordinated production capacity cuts to help alleviate Europe's car market crisis have underlined a division between Europe's money-losing mass market carmakers, including Fiat, and their better-performing German rivals.
Marchionne confirmed after an ACEA board meeting at the Paris auto show, that he had not quit. "We're good friends," he said, referring to Volkswagen Chief Executive Martin Winterkorn, as they embraced for a photo.
Relations between German automakers and others are also strained by their contrasting situations - with overcapacity concentrated in France, Spain and Italy - and divergent interests in areas ranging from European CO2 regulations to trade policy.
Marchionne said on Friday that the ACEA board had agreed all member companies would reach individual decisions on issues like plant closures.
"There is no common position on this matter at ACEA, other than dealing with regulatory issues."
An industry source told Reuters Volkswagen still wanted a longer-term revamp of ACEA's structure that would see an end to the rotation of its presidency among carmakers. Instead, VW wanted the presidency transformed into a permanent, neutral role, the source said.
VW sales chief Christian Klingler defended the company's pricing strategy on Thursday, saying it was doing well financially. "That shows we treated the issue of pricing with great sensitivity and we will continue to do so in future.
Marchionne had said on Thursday he would be prepared to resign from ACEA if he lost support of the board.
(Additional Reporting by Laurence Frost; Writing by Helen Massy-Beresford; Editing by Elaine Hardcastle)
(helen.beresford@thomsonreuters.com; +44 207 542 3112; Reuters Messaging: helen.beresford.thomsonreuters.com@reuters.net)
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