Andy Burnham today urged Scots to 'move beyond' the question of independence as he despaired at how 'too much time is wasted on those dramas'.
The Prime Minister, speaking in Motherwell, made clear his support for Scotland remaining part of the UK as he offered 'deeper' devolution to the country.
He said he wanted to 'move on from the old politics of conflict' between London and Edinburgh with a 'serious and genuine offer' to the Scottish Government.
But critics questioned Mr Burnham's plea to 'move forward' from the issue of Scottish independence at the same time as he is reviving rows over Brexit.
As well as bidding for closer ties with Brussels at a UK-EU summit next month, the PM has also said he wants a debate over Britain's longer-term relationship with the bloc.
Mr Burnham has failed to rule out a future Labour election manifesto including a promise to rejoin the EU.
Andy Burnham today urged Scots to 'move beyond' the question of independence as he despaired at how 'too much time is wasted on those dramas'
The Prime Minister, speaking in Motherwell, made clear his support for Scotland remaining part of the UK as he offered 'deeper' devolution to the country
During his visit to North Lanarkshire on Friday, the PM did not directly rule out a second Scottish independence referendum during his premiership.
But he said he had set out his views on the issue 'very clearly' to Scottish First Minister John Swinney.
'I think unions of countries are better because you can face a challenging world in a more confident and stronger way, in my view, when you collaborate and you work together,' Mr Burnham said.
He added that Mr Swinney 'has a different view, but let's accept there's a different view there and then work on together what we can agree on'.
'My view won't be changing, but let's now move forward where we can make some progress,' the PM continued.
Mr Burnham also urged politicians to 'move beyond the constitutional questions' and 'focus on solutions for people right now'.
Asked whether his bid to devolve power more locally in Scotland would make independence more or less likely, the PM said: 'I just feel we all have to move beyond the constitutional questions.
'In my view, people in Scotland are suffering from the cost of living crisis, like they are in England and everywhere else, and I think our job is to focus on the practicalities, to focus on solutions for people right now.
'As I said at the end, too much time is wasted on those dramas, it consumes too much energy.
'Get into the things that can make a difference in people's lives now, get doing the things that can take young people off benefits in their 20s and give them an opportunity now, we can do it.
'And do things to help people with the cost of living now, putting buses under public control in Glasgow or elsewhere. We can do it now and help people.'
The PM promised a 'serious and genuine offer' to the SNP-led Scottish Government to work together on devolving power.
'We won't agree on everything, and we're not going to, and we shouldn't try because there are some things we will disagree on,' Mr Burnham said.
'But that does not mean, just because you can't agree on everything, it doesn't mean you can't agree on anything.
'We can agree on some things and I know that because I've worked with John over a long period of time.'
He added: 'I want to make a serious and genuine offer to the Scottish Government. I want to move on from the old politics of conflict.'
Mr Burnham failed to confirm if the UK Government would give the go-ahead to new oil and gas drilling at the Jackdaw and Rosebank fields in the North Sea.
The PM, who has promised to take a 'pragmatic' approach to fossil fuel production, only said a decision would come 'in due course'.
Responding to Mr Burnham's comments in Motherwell, Tory former Cabinet minister Jacob Rees-Mogg told the Mail: 'Burnham wants to gut the nation state with power to Brussels or the regions, leaving nothing for him to do.
'Is he idle or simply unaware of the consequences of his actions?'
Scottish Tory leader Russell Findlay said: 'On his rare visit to Scotland, Andy Burnham should have been giving the green light to new drilling.
'But instead he was droning on about abstract political structures and procedures.
'Burnham has again opened the door for John Swinney to demand another divisive referendum.'
In a statement to the House of Commons on Monday, the PM said he wanted to use the UK-EU summit in 20 November to show he is 'open to a discussion about our relationship with the EU in the longer term'.
He claimed the 'status quo is not good enough for Britain' and it would be 'a major dereliction of duty to turn away'.
Former Labour leader Neil Kinnock this week declared Mr Burnham will be the PM to take Britain back into the EU.