Nissan's Sunderland's car plant is Britain's biggest, now on the sidelines of Brexit, this carmaker wants UK to pledge compensation for any tax barriers that may be raised as a result of leaving the European Union.
Carlos Ghosn of Nissan said it could not afford to "wait until the end of Brexit" for a deal.
On the other hand, Dr Ralf Speth of Jaguar Land Rover responded by saying his company would have to "realign its thinking" on investment if Nissan was to get any kind of compensation - insisting there should be a level playing field.
He also told the Reuters news agency there had been signs of a backlash in Europe, the firm's largest market, after the EU vote with some continental customers no longer wanting to buy British cars.
The pair spoke up amid warnings from Britain's car industry body that investment was being hit by uncertainty following the Leave vote.
The Sunderland plant is Nissan's biggest factory in Europe, with a capacity of 500,000 vehicles a year.
It represents around a third of Britain's total car output.
The plant's 6,700 workers turn out Juke, Qashqai and Leaf models, many of them for export to the continent.
Nissan is due to decide early next year on where to build its next Qashqai vehicle.
There are fears among carmakers that Britain could be heading towards a "hard Brexit" which would leave them paying tariffs to export UK-made cars to Europe.
Mr Ghosn told reporters at the Paris motor show: "If I need to make an investment in the next few months and I can't wait until the end of Brexit, then I have to make a deal with the UK Government.