Boris Johnson has said “there is a way” of getting a Brexit deal as he prepares to discuss his options with Democratic Unionist leader Arlene Foster.
The PM, whose attempts to force an early election have been blocked by MPs, said “loads of people” wanted an agreement but he was prepared to leave without one if “absolutely necessary”.
The DUP said any solution which led to UK trade borders was a “non-runner”.
Parliament was dramatically suspended for five weeks earlier on Tuesday.
MPs are not now due to return to Westminster until 14 October after Parliament was controversially prorogued.
Amid unprecedented scenes in the Commons early on Tuesday, some MPs protested against the suspension with signs saying “silenced” while shouting: “Shame on you.”
Mr Johnson dismissed as “a load of nonsense” claims that proroguing Parliament was undemocratic. adding: “We were very, very clear, that if people wanted a democratic moment, if they wanted an election, we offered it to the Labour opposition and mysteriously, they decided not to go for it.”
Opposition MPs said a law blocking a no-deal Brexit on 31 October must be enforced first before there could be any election.
Mr Johnson has insisted he will not ask the EU for a further delay but, after legislation passed by MPs, he will be legally obliged to do so unless Parliament approves an agreement by 19 October.
Key sticking point
Ahead of their talks in Downing Street, the DUP insisted their influence over Brexit events was “not waning” despite Mr Johnson’s government losing its Commons majority.
The party, which propped up Theresa May’s government since the 2017 election, said it would not support any revised version of the former PM’s Brexit agreement which separated Northern Ireland from the rest of the UK.
The Irish border has proved a key sticking point in attempts to agree a Brexit deal between the UK and the EU.
The government has indicated it could support harmonised rules for the agriculture and food sector to prevent the need for any sanitary and other health checks on the border between Northern Ireland and the Republic.
But it has distanced itself from reports that plans for a single EU-UK customs territory in the current withdrawal agreement – rejected three times by MPs – could be replaced with a specific Northern Ireland only “backstop” arrangement.
Sir Jeffrey Donaldson said a considerable number of Tory MPs would look to the DUP to judge the likely success of any new proposals.
“We are plugged into the ongoing discussions about alternative arrangements, we have a significant role to play and, therefore, I would argue that our influence remains,” he told Radio 4’s World at One programme.
“I don’t see the prime minister, who appointed himself as the minister for the Union, agreeing to an arrangement that separates Northern Ireland from Great Britain in trading terms,” he said.
“I think that this idea that you have a Northern Ireland-only backstop where you have a trade border in the Irish Sea between Northern Ireland and Great Britain is simply a non-runner.”