SNP MPs would back a new Brexit referendum if it were put to them, party leader Nicola Sturgeon has said.
Campaigners have been pressing for a fresh vote on whatever exit plans result from talks with EU leaders.
Labour has not ruled out supporting a so-called People’s Vote, and some Tory MPs back the idea, although it has been ruled out by Theresa May.
Ms Sturgeon said SNP MPs would oppose anything short of staying in the single market and customs union.
The UK is due to leave the EU on 29 March 2019, but negotiations on an exit agreement have been bogged down over the future of the Irish border and the future financial relationship.
Both sides have been making contingency plans in the event of no deal being reached, but Ireland’s Deputy Prime Minister Simon Coveney told Sky News the chances of getting an exit agreement were “good”.
Talks on this element were about 90% completed, he said, predicting a “bumpy ride” but adding: “I think it can be done.”
The UK and the EU had hoped to finalise this so-called divorce agreement and agree a statement on future economic co-operation at an EU summit on 17 October, but EU officials say it may be November before a deal can be reached.
This would then be put to MPs in a vote at Westminster, as well as being ratified by the remaining EU member states.
Speaking on the BBC’s Andrew Marr Show ahead of the opening of the SNP conference in Glasgow, Ms Sturgeon, the Scottish first minister, said her party would oppose anything short of membership of the EU single market and customs union – both of which have been ruled out by Downing Street.
The UK was heading for a “cobbled together” exit agreement, she said, which would be “almost as unacceptable as no deal at all”.
She said MPs would come together to avoid a “fire or frying pan” situation.
Analysis by BBC political correspondent Nick Eardley
In an age of political shocks, Nicola Sturgeon backing a new EU referendum won’t count as one of the biggest.
The party had always said it was open to the idea, even if it still has concerns you could end up with another situation where Scotland votes Remain, but ends up bound by a UK-wide result.
It makes the SNP – with its 35 MPs – the biggest party in Parliament to back a so-called “people’s vote”.
But the Commons numbers who have committed to supporting one still remain a small minority.
The government has ruled one out. Labour says it’s still an option – but it isn’t their preference.
So campaigners who want the public to have its say on the final deal still have a lot of work to do if they are to get their wish.
Ms Sturgeon predicted any deal brought back from Brussels would be a “fudge”, which would be almost as bad as no deal at all.
“I think in those circumstances, sensible MPs of all parties should come together to look at the alternative,” she said.
“No doubt calls for a second referendum would grow in those circumstances, and I’ve said before we wouldn’t stand in the way of a second referendum. I think SNP MPs would undoubtedly vote for that proposition.”
Ms Sturgeon also said the Article 50 deadline of the UK leaving the EU in March 2019 should be extended if necessary, to allow more time for talks.
Last week Theresa May told the Conservative Party conference that the June 2016 referendum had been the real “people’s vote”, adding: “A second referendum would be a ‘politicians’ vote’ – politicians telling people they got it wrong the first time and should try again.
“Think for a moment what it would do to faith in our democracy if – having asked the people of this country to take this decision – politicians tried to overturn it.”
Pop stars’ Brexit warning
Meanwhile several leading musicians have warned that Brexit threatens to place the country in a “self-built cultural jail”.
A letter to the Observer orchestrated by Bob Geldof and backed by stars including Ed Sheeran, Rita Ora and Sting, says leaving the EU will have an impact on touring, royalties and copyright.
It is EU free movement, the letter says, which allows “our cultural warriors, to wander Europe and speak of us to a world that cannot get enough of [them], and which generates countless billions for our threatened institutions”.
“We must take back our future” and reform the EU, it adds, without proposing a specific course of action.
SNP conference begins
Thousands of delegates will gather at the Scottish Event Campus in Glasgow for the SNP conference, which will include motions on reusable plastic, compulsory CPR training in schools and the devolution of migration policy.
There will be no discussion of independence or a second referendum in the main conference hall – although both will feature at fringe events and in speeches from party figures including deputy leader Keith Brown and Westminster group leader Ian Blackford.
Speaking to Andrew Marr, Ms Sturgeon repeated that she would set out her views on the prospect of a second Scottish independence referendum once there is clarity about Brexit.
She previously called for another vote on independence immediately after the EU referendum in 2016, but her plan was temporarily shelved after the SNP lost 21 seats in last year’s general election.
Tens of thousands of independence supporters – including Mr Brown – marched through Edinburgh on Saturday in the latest in a series of rallies aimed at ramping up pressure for a second referendum to be held.