Ferrari have been involved at the top of Formula One since 1950
Ferrari are threatening to review their participation in Formula One if plans to introduce a standard engine for all teams go ahead from 2010.
F1's governing body the International Automobile Federation (FIA) wants to bring in the rule to save costs.
"The use of same engines would deprive F1 of its competition and technological development," said Ferrari.
"The board reserves the right to consider, together with our partners, our presence in this discipline."
The FIA played down the row on Tuesday, saying in a statement: "The FIA has noted the press statement issued by the Ferrari board of directors. It seems the Ferrari board were misinformed.
"The FIA has offered the teams three options, one of which is the so-called standard engine, and another that the manufacturers should jointly guarantee to supply power trains to the independent teams for less than 5m euros per season.
It's a real threat that the teams are united here - that the boards are united behind their teams - and that the FIA are not going to be able to steamroller their plans through
"The FIA is delighted by Ferrari's financial success and hopes this will be maintained. However a number of teams find themselves facing costs which greatly exceed income. This is not sustainable.
"It is now for the manufacturers to agree one of the three FIA options or themselves produce concrete proposals to reduce costs to a sustainable level.
"If neither happens, the FIA will take whatever measures prove necessary to preserve a credible world championship for both drivers and constructors."
In July, FIA chief Max Mosley said F1 was becoming increasingly "unsustainable" while urging teams to find ways to reduce both their costs and fuel consumption.
F1 supremo Bernie Ecclestone does not believe major car manufacturers would quit the sport over the standard engine issue.
I don't think any of the manufacturers want a homogenised engine
Toyota Motorsport president John Howett
"I don't see why they should leave. We are saving them an awful lot of money, I hope. I don't see why they should," said Ecclestone.
"Why should someone pull out because they are going to save a lot of money? All the technical things will still be there so they can show all their talents.
"What we want is to reduce the necessity to spend to be competitive. That is the simplest thing."
However, BBC 5 Live commentator David Croft believes there is a possibility that the teams could stand firm and refuse to back the FIA's proposal.
"It's a real threat that the teams are united here - that the boards are united behind their teams - and that the FIA are not going to be able to steamroller their plans through," said Croft.
"The Formula One Teams Association (FOTA) has already said 'we're not going to supply engines in the tendering process,' so who's going to make these standardised engines?
"They support Max Mosley in the cost-cutting plans, it has to happen, but they're not going to do it off the back of standardised engines."
Toyota Motorsport president John Howett has already come out in support of Ferrari's demand for different engines for the teams.
"I don't think any of the manufacturers want a homogenised engine," said Howett.
"If it is forced through, then it (quitting) is not a decision we will take here (Toyota F1's base in Cologne).
"It will be taken by the board in Japan, but they want a degree of differentiation between teams."
Before this month's Chinese Grand Prix the FIA announced a tender for "a third-party supplier of engines and transmission systems" to be used by all teams in 2010, 2011 and 2012.