Business Secretary Greg Clark has said there are "grounds for optimism" that the UK will strike a Brexit deal with the EU.
It comes as leading Conservative Brexiteers urge the prime minister to ditch her Chequers plan in favour of a Canada-style agreement.
Theresa May said her proposals, which were rejected by EU leaders at a summit in Salzburg, remain the only viable option for an exit agreement.
Mr Clark told BBC Radio that "of course we want a deal", adding that there "are grounds for optimism that we can can reach an agreement".
He added: "No one should be under any illusion that the prime minister and our negotiating team are absolutely determined and recognise of course that we need to have a deal, that we want to have the best deal that will allow not just the success at present be enjoyed but for us to grasp this opportunity."
The business secretary was responding to comments from the boss of Toyota's plant in Burnaston, Derbyshire.
Marvin Cooke told the BBC said the company might have to halt production for "months" if an agreement is not reached, potentially putting jobs at risk.
The plant produced 144,000 models in 2017.
Mr Cooke said: "If we crash out of the EU at the end of March the supply chain will be impacted and we will see production stops in our factory.
"We cannot predict if the impact of a hard Brexit would be hours, days, weeks or months, so we cannot predict whether or not such interruptions would continue for just a few hours, days or months.
"In the past, of there has been a minor problem with a vehicle or at the (Channel) Tunnel, we can overcome it, it's a minor impact.
"This is unprecedented, totally unknown."
Mr Cooke's words are the latest in a series of warnings from car-makers that any delays at borders could slow the movement of components and finished models, adding costs and crippling output.
Other car-markers in Britain, including BMW, McLaren and Honda, said they had triggered some Brexit contigency plans, such as certifying models in the EU.
They added they were working on redrawing production schedules and stockpiling more parts.
This will ensure plants, which rely on the just-in-time delivery of tens of thousands of components, can keep operating after Brexit.
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But the measures will add costs and bureaucracy which could risk their long-term viability.
Jaguar Land Rover, Britain's biggest car-maker, has warned it does not know whether its plants will be able to operate in six months' time and that the wrong Brexit deal could cost thousands of jobs.
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