While Scottish Labour leader Richard Leonard attempted to quell the row sparked by the Shadow Chancellor yesterday, saying a second referendum was "unwanted and unnecessary", Mr McDonnell repeated his view that he would not use "parliamentary devices" to prevent a vote.
He said his position was backed by Jeremy Corbyn, and that there was now a "debate" around how the party should go forward in terms of dealing with SNP demands for a second referendum.
Current Labour policy is to oppose a second independence referendum, and Richard Leonard has said that a Labour government would not grant the Section 30 order needed for one to be held.
However Mr McDonnell today said he would not be "set up" by Nicola Sturgeon into arguing the UK government would stand in the way of another referendum.
Speaking at an Edinburgh Fringe event, where he was interviewed by journalist Graham Spiers, Mr McDonnell was asked about his remarks yesterday on Scottish independence, which ignited a furious row in his party.
He said: "What I said yesterday, that was not picked up, is actually what I want is a Labour government, and let us demonstrate as a Labour Government what we can do to transform people's lives, and if, after a few years, people come back and say they want to test the water on an independence referendum then fair enough, that's up to the Scottish people and the Scottish Parliament. I'm not here to block a democratic exercise by any means.
"For me, the priority is a Labour Government. If the Scottish Parliament and the Scottish people determine that they want another referendum, I'm not being set up by Nicola Sturgeon because that's what she's trying to do. She's trying to say it's the big bad English yet again trying to prevent us holding a referendum.
"No we're not. What we're saying is it's unnecessary. We will campaign against having a referendum, but we are not using parliamentary devices to block it — it's as simple as that."
He added that he was on the same page as Edinburgh South Labour MP Ian Murray, who was fiercely critical of Mr McDonnell's remarks, saying: "I'm arguing for a United Kingdom, I'm arguing for a Labour government that will address the needs of working people, in Scotland and across the UK, which will demonstrate that the referendum issue and independence is irrelevant."
Asked if he had changed his party policy "on the spot", as it was in direct contrast to the manifesto commitment, Mr McDonnell appeared to suggest the party was internally looking to change the commitment to opposing a second referendum ahead of the next general election.
He said: "In manifestos there's always different views and we have a democratic process to decide it, and in my view as we go forward in our discussions my view is we should argue against a referendum and concentrate on getting a Labour government elected, and we shouldn't be set up by Nicola Sturgeon on this issue.
"That's the debate we're now having in how we go forward, and m view is that we shouldn't be manipulated by Nicola Sturgeon in that referendum debate by trying to accuse a UK parliament of trying to block the will of the Scottish people - better for us to argue for the need for a Labour government and that a referendum doesn't help the process, it impedes the process, of improving people's lives.
Mr McDonnell also said that he had had a "conversation" with Richard Leonard who "understands where I'm coming from and is on the same page as me about achieving a Labour government."
Yet in March this year Mr Leonard had insisted a future Labour government would block a second referendum, even if the Scottish Parliament requested the Section 30 power to hold it.
In a statement Mr Leonard said he'd met with Mr McDonnell this morning - but he did not repeat his March position. He said: “I met with John this morning, and I made clear to him that a second independence referendum is unwanted by the people of Scotland and it is unnecessary. The 2014 referendum was a once in a generation vote.
“There is no economic case for independence, especially with the SNP’s new position of ditching the pound and new policy of turbo-charged austerity to bear down on the deficit. On that John McDonnell and I are in firm agreement - what Scotland needs is radical reforming Labour governments at Holyrood and Westminster.”
The confused position, has seen party members row over policy on social media. A group of 13 Scottish Labour candidates said they were clear in their opposition to a second referendum, while others, including Neil Findlay MSP, have said John McDonnell is "absolutely right".
Asked what he made of the reaction of party members to his remarks, Mr McDonnell said: "I think the members will recognise that what I'm about is maintaining the union and overcoming any of the arguments that could be mobilised by the SNP, or others, to undermine the union and the best way to do that is to secure a Labour government.
"But we cannot allow ourselves to be deflected by being set up by the SNP to say we put the proposals but this wicked UK government, under Labour, prevented this happening. We're saying we respect democracy but the real issue is the levels of poverty and security and of public service. For Labour members that's what we want to campaign on and we don't want to be sidelined by another referendum, that's why we argue against it.
"But there's a large number of people, Labour supporters, who voted yes in the last referendum and we need to have a conversation with them to ensure they know what Labour is all about, addressing the real issues, not a constitutional cul-de-sac."
He also said he had slipped up yesterday in referring to Westminster as the "English parliament", when he had meant "English parliamentarians".
Scottish Liberal Democrat leader Willie Rennie said Labour was “scheming on independence, just like they are on Brexit”.
He said: “Richard Leonard was unable to persuade John McDonnell that he was wrong on supporting another independence referendum. This confirms that the Shadow Chancellor’s comments at the Edinburgh Festival were no mistake and he meant every word.
“Labour is scheming on independence just like they are scheming on Brexit. They are prepared to trade on both to get into power. Boris Johnson is getting organised and is careering towards a damaging Brexit so time is short.
“The role of the Liberal Democrats in standing up our partnerships with our neighbours in the UK and Europe has never been more important.
“Progressives should come with the Liberal Democrats to stop these vandals who are determined to wreck our country.”
And SNP MSP Jenny Gilruth said: “With a No Deal Brexit approaching, we urgently need clarity from Richard Leonard and Scottish Labour. It’s a bit embarrassing that Westminster Labour politicians have done more than their Holyrood colleagues to defend the democratic rights of the people of Scotland.“They’re more interested in siding with the Tories and fighting with each other than defending Scotland’s interests. That explains why people across Scotland have given up on Richard Leonard’s party, and why they’re polling in single figures. Voters just can’t take them seriously anymore.“As polls show, more and more people are drawn to the opportunities of independence. Unless Scottish Labour join the SNP in defending Scotland’s right to hold an independence referendum, they’ll be lending their backing to the a jobs-wrecking Tory Brexit and will continue their slide into complete irrelevance.”