Scotland for a People’s Vote held a cross-party news conference in Edinburgh, with former Scottish Labour leader Kezia Dugdale among the speakers, along with SNP MP Tommy Sheppard, Liberal Democrat MP Christine Jardine and Andy Wightman, the Greens' Lothians MSP.
The group has stepped up campaigning with just over five weeks before the March 29 Brexit deadline and are adamant a second vote will win the backing of the Commons.
EU leaders have indicated they would be prepared to delay the UK's departure from the EU to allow such a Peoples' Vote to take place.
Mr Sheppard said: "Of all the options still on the table, this is the one that probably has the most support in terms of Parliament. Not yet expressed in a majority but in my reckoning a lot closer to a majority than either No deal or Theresa May's Withdrawal agreement.
"I think putting that together will involve some members of the Conservative party, some of whom have already put their heads above the parapet, others of whom are hedging their bets and waiting until the clock runs down a little more, but they will come round to this position I think in the next few weeks."
Today's event at the Scottish Poetry Library in Edinburgh was was haired by John Edward, former Head of the European Parliament Office in Scotland. It followed the announcement over the weekend of plans for a massive demonstration in London on Saturday March 23, just six days before the UK is currently scheduled to leave the EU.
Ms Jardine, the Liberal Democrat MP for Edinburgh West added: "There is increasingly a majority who are looking for a way forward and the Peoples Vote is seen as the way forward.
"It's seen as a way of breaking the logjam and I'm confident that in the next couple of weeks, we will have a situation in the Commons where we are able to vote on that properly for the first time with a clear mandate to do so and we will see a majority formed to get back to the people and say is this what you wanted? Or is the situation now very different from what it was two and a half years ago."
The campaign points to consistent polling which suggests a majority would now vote to remain in the EU.
Ms Dugdale said: “I remain deeply concerned about the impact Brexit will have on jobs and the economy, knowing that the pain will be borne by the people least able to afford it."
The Scottish Parliament already voted for a motion in favour of a People’s Vote.
Mr Wightman added: “The Scottish Green Party is part of a global and European family of green parties. We believe in a Europe that co-operates and works together to build a better future, tackle the threat of climate breakdown and consolidate human rights and the rule of law across the continent."