Dieter Zetsche, chief executive of Daimler, said the company might miss the target of emitting 95 grams of CO2 per kilometre because of scant public appetite for electric cars.
Sergio Marchionne, chief executive of FCA, said government mandates for electric car sales were required for carmakers to comply with the rules.
“It’s the only way that we’re going to make the numbers,” he said on the edge of the Detroit Motor Show.
Mr Zetsche, who is also at the show, said Daimler aimed to meet the rules, but that “not every parameter is under our control”.
He added: “I can’t guarantee we will be compliant”.
Carmakers across Europe are grappling with the new rules, which are more difficult to hit because of the collapse in sales of diesel cars, which emit about a fifth less CO2 than petrol.
Sales of petrol cars in Europe overtook diesel in 2017 for the first time since 2009.
At the same time, sales of electric cars remain sluggish with the majority of sales driven by government tax incentives.
While almost all of the major brands are launching electric models in the next three years, the industry believes a fall in battery prices and a larger number of charging points are also required before the vehicles become as attractive to motorists as internal combustion engine cars.
Carmakers face stiff penalties for missing the 2021 targets, with a fine of €95 for every gram over 95 grams.
Analysts have said that several carmakers are on course to receive fines in the hundreds of millions of euros.
Mr Marchionne said the potential fines were so severe that carmakers may be forced to stop selling some models in order to comply.
“We’ll just stop selling cars,” he said, before adding that FCA will meet the targets and so will not have to stop sales.
Carmakers that miss the target also risk a public backlash, Mr Zetsche said.
“There might be some reputational aspect in there as well,” he added.
Mr Marchionne, who has been a long-time critic of the hype surrounding electric cars, said there are “unrealistic expectations of where this industry will go”.
He added: “It will happen . . . but it will take a lot longer.”
Last year many of Europe’s largest carmakers issued ambitious targets for electric vehicle sales, though several admitted that the cars would make less profit than traditional petrol or diesel vehicles.
VW said it would make 50 new electric vehicles by 2025, while Daimler expects that between 15 per cent and 25 per cent of its sales will be fully electric cars in 2025.
Ford on Sunday significantly increased the amount it would invest in electric cars, to $11bn from a previous figure of $5bn. The company promised to make 16 fully battery electric vehicles by 2022 and 24 hybrid and plug-in vehicles.
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