PARIS – Bad blood continues to flow between Volkswagen and Fiat at the auto show here, where Fiat/Chrysler CEO Sergio Marchionne issues a challenge of sorts to the German auto maker following calls for him step down as head of the ACEA, the European car makers group.

The ACEA, which is run by a board made up of CEOs of its member companies, is meeting at the show today to discuss issues plaguing the industry, and Marchionne says if VW wants him removed as the group’s head, then CEO Martin Winterkorn should attend the meeting and lobby for his ouster.

Winterkorn has not suggested Marchionne be broomed out as this year’s ACEA head, but lower- level officials at the auto maker have done so, including its chief financial officer.

“If Mr. Winterkorn ever shows up at one of these meetings, he can decide to express the view to the board, (which) will decide if I should be chairman,” the Fiat CEO says. “I do (the job) on behalf of everyone who is a member of the association. I have no particular interest in continuing my role without the support of the board.

“But I also don’t particularly (care) what the CFO or the head of the press office of Volkswagen thinks. They can take their opinions and park them in China.”

The ongoing spat has hit a crescendo in recent weeks, as Marchionne pointed a finger at VW’s aggressive pricing amid Europe’s market downturn, which he suggests is contributing to the financial struggles of some auto makers.

Europe has too much capacity, and Marchionne has suggested the European Union get involved in ways to reduce production volumes, because no country within the EU wants to see any of its plants shuttered and jobs lost.

The Fiat CEO says he could make a valid economic case for why facilities should be closed in Germany, where no assembly plant has been idled since World War II. That has raised the ire of VW insiders.

Marchionne also says he is disappointed with VW’s rhetoric in recent days, saying the company has violated a code of ethics among ACEA members in discussing other auto makers’ business situations. He says as the group’s top official, only he is authorized to comment on industry-wide issues.

If VW was to lead a coup for his ouster, Marchionne says Fiat could quit the ACEA altogether.

The Fiat CEO’s outlook on European sales industry-wide is decidedly bearish, predicting volume will be flat or even below this year’s levels. That could make plant closings more likely, he says, “but I express no view on if it’s probable.”

If action isn’t taken, “We’ll end up with a whole pile of state-owned enterprises,” Marchionne warns. “And I guarantee you that five years from now, instead of seeing all those beautiful cars you see out there (on the show floor), you will see a bunch of boring, gray Trabants.”