The Prime Minister was accused of ‘opening the door’ to another divisive independence referendum after failing to rule out a fresh vote during his premiership.
During a keynote speech in Motherwell, Andy Burnham declined to explicitly rule out a second referendum, saying only that his view on independence “won’t be changing”.
Mr Burnham was delivering his first major speech in Scotland since becoming Prime Minister at New College Lanarkshire’s campus in Motherwell, built on the site of the old Ravenscraig steelworks.
Scottish Conservative leader Russell Findlay said: 'Burnham has again opened the door for John Swinney to demand another divisive referendum.
'On his rare visit to Scotland, Andy Burnham should have been giving the green light to new [North Sea] drilling. But instead, he was droning on about abstract political structures and procedures. All of this is a massive distraction which won’t create a single job, apart from more jobs for the boys.'
A source close to the First Minister said he was 'surprised' Mr Burnham had not categorically ruled out a referendum.
Economy Secretary Stephen Flynn went further and described Mr Burnham’s comments as a 'very significant moment in Scotland’s constitutional journey'.
Andy Burnham was in Scotland at the same time as the SNP was holding its annual conference in Aberdeen
During a question and answer session with the press after his speech, Mr Burnham was asked whether he would rule out a second Scottish independence referendum for the duration of his premiership.
He replied: 'I’m somebody who believes in all forms of unions, trade unions, definitely, and I think unions of countries are far better because you can face a challenging world in a more confident and stronger way in my view, when we collaborate and work together.'
He said he had made his position clear to Scottish First Minister John Swinney, adding: 'He has a different view. But let’s accept there’s a different view there, and work on what we can agree on.'
He continued: 'My view won’t be changing, but let’s now move forward where we can make some progress.'
Mr Flynn said: 'What I just listened to was the Prime Minister of the United Kingdom being asked whether he would rule out an independence referendum and he declined to do so.
'I firmly believe he declined to do so because he is a reasonable man who recognises his own hypocrisy if he was to continue along the lines of saying there can and should be a debate about a second referendum on membership of the European Union while seeking to deny one to the Scottish people in respect of our future.'
He added: 'He has again today outlined that he is not opposed to that second independence referendum, very much building upon what he of course said in the House of Commons, and I think this is a very significant moment in Scotland’s constitutional journey.'
Speaking in the House of Commons last month, Mr Burnham said the rules governing when a second Scottish independence referendum could take place should be 'exactly the same' as those for an Irish reunification referendum.
However, he later said a second Scottish independence referendum was 'off limits'.
Mr Burnham was in Scotland at the same time as the SNP was holding its annual conference in Aberdeen.
In a speech focused on increasing devolution in Scotland, Mr Burnham called for an end to 'tribal politics' between Holyrood and Westminster, urging Mr Swinney to move beyond the constitutional question and focus on 'solutions for people right now'.
He described Scotland as 'one of the most centralised nations in Europe' and called for 'deeper devolution' north of the border.
He said: 'Devolution was never supposed to stop at the doors of the Scottish Parliament.'
Mr Burnham said he would set out plans for a 'new deal' for regional economic development in the coming months. The proposals are expected to include an offer of further devolution from the Department for Work and Pensions.
He also called on Mr Swinney to transfer more powers from Holyrood to local areas.
The Scottish Government announced plans last month to overhaul regional governance, replacing the current 32 local authorities with six new regional authorities.
However, details of how the proposed system would operate have yet to be released. Trade unions and SNP councillors have raised concerns that the changes could reduce local accountability.
Mr Swinney said he was willing to work with the Prime Minister if he devolved more powers to Scotland.
He said: 'I’m all for the Scottish Parliament having as many powers as it possibly can do, and I’ll work constructively to make sure we bring all those powers to Scotland.'
Mr Flynn also said Mr Swinney had written to the Prime Minister this week seeking greater powers for Holyrood, with employability powers listed at number seven on the list of requests.