There is a danger that GM Europe could be declared insolvent
Fiat has decided not to attend Friday's meeting in Berlin at which a preferred bidder for GM Europe, which owns Opel and Vauxhall, was to be chosen.
Fiat still wants to buy GM Europe, but it said German government requests for extra funding were "unreasonable".
There is now some doubt as to whether the meeting will go ahead as continuing talks between GM and rival bidder Magna are proving to be difficult.
GM in the US is expected to declare Chapter 11 bankruptcy on Monday.
There is a danger that GM Europe could also be declared insolvent if its future is not secured by then.
GM EUROPE BIDDERS' PLANS
Fiat: Italian carmaker; plans 10,000 job cuts in Europe; could close one of four Opel factories in Germany
Magna: Canadian-Austrian car parts group; Plans 2,500 job cuts in Germany; pledges to inject between 500m and 700m euros into Opel; 10% of the new company would be owned by Opel employees; GM would keep a 35% stake in the company; bid in connection with Russia's state-run Sberbank and Oleg Deripaska's truck firm Gaz
The German government had hoped to reach a decision on Wednesday, but said it needed more information from the US after GM asked for extra cash.
The sale of GM Europe is a key part of the troubled American car group's plans to restructure its business.
While GM will ultimately choose who buys Opel and Vauxhall, the German government's preference is key because Berlin has pledged the most financial support for the eventual buyer. About half of GM Europe's 50,000 workers are employed in Germany.
German officials said earlier in the week that their focus was on two bidders: Fiat and Canadian-Austrian car parts manufacturer Magna.
The US investor Ripplewood Holdings pulled out of the race on Wednesday night.
There was also a last-minute expression of interest from Beijing Automotive Industry Corp (BAIC), but German officials said they did not yet have enough information on BAIC's offer.
Now, Fiat has said it is unreasonable for the German government to ask Fiat to provide emergency funding to Opel, while it decided on the timing and conditions of its own bridge financing.
Fiat boss Sergio Marchionne said that would expose his company to "unnecessary and unwarranted risks" because it has not yet been given full access to Opel's books.
On Thursday, the German government criticised the US Treasury and General Motors after being told at the last minute that that GM Europe would need another 300m euros ($415m; £260m) in short-term funding.
It has already offered almost 1.4bn euros in loan guarantees.
European Union industry ministers will meet in Brussels on Friday to discuss GM Europe, a meeting called after some countries with GM plants said that Germany was having too much say over the future of the company.
But Karl-Theodor zu Guttenberg, the German economy minister, dismissed suggestions he was putting German jobs first, saying he had the wider interests of Europe at heart.
While GM Europe is a big employer in Germany, the UK, home of GM's Vauxhall brand, is another big employer with 5,500 jobs at stake.
Meanwhile, the GM parent company in Detroit is moving closer to bankruptcy protection backed by the US Treasury.
The board of the carmaker will meet on Friday to prepare to file for bankruptcy in New York on Monday, in what would be the biggest bankruptcy of a US company.
Under the current plan, the US Treasury, which has already loaned General Motors (GM) nearly $20bn (£12.5bn), would get 72.5% of the new company's stock.
In return, the US government would provide $30bn in additional financing to keep the new GM operating under bankruptcy protection.
GM bondholders, who hold $27bn of GM debt, are being offered the option to buy an extra 15%, on top of the 10% they had previously been offered.
If bondholders back the new offer, it will allow GM to come out of bankruptcy more quickly. GM said it had already secured the backing for the new offer from bondholders representing 20% of the bond debt.