Ministers have held discussions with Jaguar Land Rover over the possibility of state assistance for the car maker, Business Secretary Lord Mandelson has said.
But he stressed that the firm's Indian owners Tata had "the first responsibility" to ensure its survival and warned that the Government did not have "an open cheque-book" to bail out ailing private companies.
Lord Mandelson said it was too early to judge whether state help would be needed at Jaguar Land Rover, which employs around 15,000 in the UK, or other parts of the British automotive sector.
The company announced last month that it was laying off around 850 IT and engineering staff in the West Midlands by the end of the year in response to "severe" global car market conditions which are affecting the whole of the sector.
Lord Mandelson told Sky News: "I'm talking to the car manufacturers. We are analysing very carefully what is going on in the sector and we will make good judgments in good time if it is appropriate for the Government to take any action or if it is possible for us to do so.
"We are looking at the sector as a whole. I have had discussions with the owners and management of Jaguar Land Rover in particular, because they argue that they are under particular strain.
"But they have owners who are well-resourced, who have the first responsibility for sustaining the companies that they own in existence and in production for the future.
"If we judge that it is not just short-term difficulties but longer-term pressures that are operating in that sector, or in relation to that particular company, then we will consider what measure, what intervention we can appropriately make. But the time for that decision has not been reached."
The Chancellor has said the Government would do "everything that we can reasonably do" to support the car industry but he also stressed that the interests of the taxpayer were of "critical importance".
Mr Darling also said the "primary responsibility" for financing any car company lies with its owners and ministers are mindful that other industries are being hit. He continued: "We will do everything that we can reasonably do to support the industry.
"But I would just say two things - one is the primary responsibility for financing a company arises with those who actually own the company.
"We also have to be mindful not only of the fact that there are difficulties in this industry, but other industries too will be affected by this downturn.
"We also have to have regard to the interests of the taxpayer - that is of critical importance and people do need to understand that."
Lord Mandelson warned that not every private company which gets into difficulty can expect Government help. He indicated that ministers would look at a range of factors when deciding whether a company qualifies for assistance, including its general viability, the strategic importance of its sector, its technological and research standing and the impact its failure would have on jobs in the supply chain, as well as the workers it employs directly.
While he warned that there will not be "a great long list of industrial bail-outs", he appeared to indicate that car makers might have a case for help.
"The car sector - car manufacturing - is a centre of real excellence and competitive strength in our country," he said. "It is not just the car makers themselves and all those employed directly in the production of cars, it is the huge supply chain of many small and medium-sized enterprises that supply components and other elements to that very important manufacturing process.
"It is not possible just at this stage to judge whether the pressures currently operating in the car sector on those manufacturers are going to be short-lived or whether they are going to go on for longer in time than some of those car makers will be able to bear."
Lord Mandelson warned: "I don't have an open cheque-book. I don't have a cheque-book of the Government's own. It is the taxpayer's money and we have a responsibility to the taxpayer to make sure that when we intervene, either to provide bridging finance to companies or give guarantees to commercial loans offered by banks, we are doing so in a responsible and proportionate way.
"There are not going to be a great long list of industrial bail-outs. It is not right, it is not possible, we don't have the resources to undertake that as a Government.
"Whilst we are prepared to look, and prepared to help if we can, we don't have an open cheque-book for private companies to come to us and for us to bail them out.
"It is going to be a rocky road and a difficult one, but it is not one where we can secure the future of every business and every company."
Liberal Democrat leader Nick Clegg said state help for the car firm would put the Government on a "difficult slippery slope" of mounting demands.
"If the Government does decide to give this taxpayer-funded help to one company it sets a precedent and it will be very difficult to refuse that assistance to other companies," he told Sky News.
He said: "I do not want to belittle, in any way, the real problems for a country like Jaguar Land Rover. I have visited their plants myself and they do a fantastic job and are actually producing a lot of quite new innovative green vehicles.
"But it is setting the precedent, in terms of Government policy, that says 'this company deserves some money; that one doesn't'. That is quite a difficult slippery slope to navigate."