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7 October 2018, 12:26 | Updated: 7 October 2018, 12:28
Nicola Sturgeon has said her party's MPs would back a so-called People's Vote, if given the option.
Her comments come as Theresa May hopes to reach a deal this month on the post-Brexit relationship with the European Union, however it is believed this could happen later.
Calls have been made for a new referendum before March - when the UK is due to leave the union - and the SNP leader has said her MPs would back such a move if negotiations end without a satisfactory agreement.
Speaking on the BBC's The Andrew Marr Show, Ms Sturgeon 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."
The UK is due to leave the EU on March 29 2019, but issues such as the Irish border and trade have stalled talks.
An agreement was hoped to be reached at the EU summit on October 17, but officials say it could be later.
MPs would then be given a "meaningful vote" on the deal.
Ms Sturgeon also said she will make her opinion known about the case for another poll after "this phase" of Brexit talks are over.
She said: "I will set out what I think the next steps are when we are at the end of this phase of negotiations.
"Whether I like it or not - or whether anybody likes it or not - the future of EU/UK relationship is the context in which Scotland will decide that question of independence."
She added: "I will set out my views on the next steps at that stage, if that's when Theresa May comes back with the deal.
"It could be later this month, it could be November, it could be December."
A poll published in The Sun on Sunday and The Sunday Herald suggests a no-deal Brexit would see backing for Scottish independence reach 52%.
The Survation survey also shows support would be a 50/50 split if the break-up goes "as planned", while support for leaving the UK would be at 46% if there was another referendum tomorrow.
Meanwhile, a poll in The Sunday Times shows backing for Scottish independence would merely grow in the case of a no-deal Brexit - but would not find a majority.
The Panelbase survey of 1,024 voters in Scotland found support for leaving the UK would increase from 45% in September 2014 to 48%, while support for staying would fall from 55% to 52%.
Ms Sturgeon added that she believes the case for a so-called People's Vote is understandable, but the real solution for Scotland is independence.
She said: "I think we are on a journey that ends with independence. I think Brexit brings issues around this sharply into focus.
"That democratic deficit we have seen in the last two year, 62% of people in Scotland voted to remain in the EU and yet in under 200 days we are going to face exit from the EU."
All Under One Banner held a rally on Saturday which saw supporters of Scottish independence march the length of the Royal Mile to Holyrood Park.
Organisers estimated more than 100,000 people took part, while authorities put the figure at 20,000.
Scottish Labour business manager Neil Findlay said: "The First Minister isn't standing up for Scotland by continuing to threaten to divide Scotland with another referendum."
Scottish Conservative shadow cabinet secretary for constitutional relations Professor Adam Tomkins added: "Nicola Sturgeon today confirmed that the SNP is the party of the Neverendum - not just in Scotland, but across the UK too.
"Scotland voted to stay in the UK and the UK voted to leave the EU. Scotland has had enough of Nicola Sturgeon's endless complaints and demands for a rematch."
The SNP conference starts on Sunday in Glasgow.