Boris Johnson will discuss his Brexit options with DUP leader Arlene Foster later as Downing Street insisted he was working “very hard” to get a deal.
After Parliament was dramatically suspended for five weeks, the PM told cabinet he wanted to focus on domestic priorities as well as preparations for leaving the EU on 31 October.
MPs have twice rejected his call for an election before the Brexit deadline.
Opposition MPs said a law blocking a no-deal Brexit must be enforced first.
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.
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.”
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 of Ireland.
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 see what its view was on any alternative arrangements to the backstop relating specifically to Northern Ireland.
“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.”
Parliament was suspended – or prorogued – at just before 02:00 BST on Tuesday.
As Speaker John Bercow – who earlier announced his resignation – was due to lead MPs in a procession to the House of Lords to mark the suspension, a group of angry opposition backbenchers tried to block his way.
Late into the night, MPs also burst into song on the Commons benches, singing traditional Welsh and Scottish songs, Labour anthem Red Flag and hymns like Jerusalem.
During the five-week suspension, parties will hold their annual conferences but no debates, votes or committee scrutiny sessions will take place.
Boris Johnson will not face Prime Minister’s Questions until the period is over and his scheduled questioning by the Commons liaison committee on Wednesday has been cancelled.
Parliament’s suspension means MPs will not get a third chance to vote for an early election until they return, meaning a poll would not be possible until November at the earliest.
In Monday’s vote, 293 MPs backed the prime minister’s motion for an early election, far short of the two thirds needed.
At present, UK law states that the country will leave the EU on 31 October, regardless of whether a withdrawal deal has been agreed with Brussels or not.
But new legislation, which was granted royal assent on Monday, changes that, and will force the prime minister to seek a delay until 31 January 2020 unless a deal – or a no-deal exit – is approved by MPs by 19 October.
Speaking on Monday, Mr Johnson said the government would use the time Parliament was suspended to press on with negotiating a deal with the EU, while still “preparing to leave without one”.
“No matter how many devices this Parliament invents to tie my hands, I will strive to get an agreement in the national interest,” he said.
Labour, the SNP, the Liberal Democrats, the Green Party, the Independent Group for Change and Plaid Cymru said they refused to agree to an election on “Boris Johnson’s terms”.
Speaking at the TUC Congress on Tuesday, Mr Corbyn said “our priority is to stop no deal – and then have a general election”.
When the election came, he said Labour would commit to another referendum with a “credible option to leave and an option to remain”.
Sir Oliver Letwin, who last week defied Mr Johnson to vote to block a no-deal outcome and subsequently lost the Conservative whip – told BBC Radio 4’s Today he believed there was now a majority in the Commons to back another referendum.
Asked whether the prime minister would back a further vote, Mr Letwin replied: “Boris has often changed his mind about many things and that’s one of his advantages, that he’s very flexible so maybe he can.”
Mr Johnson is now more than 20 seats short of a majority in Parliament, making effective government extremely difficult.
The prime minister’s self-imposed Halloween Brexit deadline looks further out of reach than a few short days ago.
Is it impossible? Absolutely not.
There is the possibility, still, of a deal, with Number 10 today stressing it was still their primary aim.
Whispers again about a Northern Ireland only backstop, and a bigger role for the Stormont assembly, if it ever gets up and running, are doing the rounds.
Some MPs and some diplomats are more cheerful about the possibilities of it working out.
If you squint, you can see the chance of an agreement being wrapped up at pace, although it seems the chances range somewhere between slim and negligible.
Read more from Laura.