“Political will” is needed for the UK and EU to agree a post-Brexit trade deal, says Dominic Raab.
The foreign secretary said the situation was “finely balanced” after negotiations between the two sides carried on through the night.
But he said the EU would need to change its position for progress to be made.
Boris Johnson and European Commission president Ursula von der Leyen are due to speak at 11:00 GMT to decide if a deal can be done.
Earlier this week, the two leaders set a deadline of Sunday to decide whether to abandon negotiations or keep them going.
But both sides have warned they are unlikely to reach an agreement.
Taoiseach (Irish prime minister) Micheál Martin said he believed a no-deal scenario “would be very bad news for all of us” and “an appalling failure of statecraft” on both sides.
The main sticking point in the talks is how close the UK should stick to EU economic rules in the future.
The EU is determined to prevent the UK from gaining what it sees as an unfair advantage of having tariff-free access to its markets – not paying taxes on goods being bought and sold – while setting its own standards on products, employment rights and business subsidies.
Fishing rights is another major area of disagreement, with the EU warning that without access to UK waters for EU fleets, UK fishermen will no longer get special access to EU markets to sell their goods.
But the UK argues that what goes on in its own waters, and its wider business rules, should be under its control as a sovereign country.
Mr Raab said that at this stage of negotiations, “what really matters is the political will”.
He told the BBC’s Andrew Marr programme: “The bar is quite high for us to be able to keep talking. We would need at a political level a commitment to move on those two key issues.
“Never say never because EU negotiations can often drag and drift. But actually we do need finality and therefore we need at the political level of Ursula von der Leyen that there is clarity the EU will move on those two key issues.
“If we get that then there are still talks to be processed.”
But Labour’s Ed Miliband accused the government of being “ideological” over its position in the talks, and warned leaving without a trade deal would be “disastrous for the country”.
He told Andrew Marr: “[The prime minister] has been cavalier with our national interests and is playing Russian roulette with jobs and livelihoods of people up and down the land.”
What happens next with Brexit?
Philip Rycroft, who was a civil service head at the UK Department for Exiting the European Union between 2017 and 2019, told BBC Breakfast things were “looking a bit grim” for a trade deal.
“Frankly, the energy seems to be draining out of this,” he said. “I think if we were heading for a deal you’d be seeing a lot more diplomatic activity – there would be signs of a lot more conversations going on.”
But Irish PM Mr Martin told Andrew Marr the fact talks had gone overnight gave him “hope” there would be agreement.
He called for the teams “with any bit of energy we have left [to] focus on negotiating a deal”.