Speaking at an event in Motherwell, North Lanarkshire, Mr Burnham said “my view won’t be changing” on another referendum.
But the Prime Minister was not explicit in his rejection of another vote, leading to Scottish Economy Secretary Stephen Flynn claiming he has not ruled out a referendum in his premiership.
When asked, Mr Burnham did not directly respond but said he had set out his views on the issue “very clearly” to John Swinney.
Stephen Flynn claimed the Prime Minister failed to rule out another referendum in his premiership (Jane Barlow/PA)
PA Wire
The Prime Minister said: “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.”
He said he had communicated his view to Scotland’s First Minister Mr Swinney.
Mr Burnham said: “He 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.”
But the Prime Minister added: “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.”
Speaking to journalists at the SNP conference in Aberdeen on Friday, Mr Flynn said: “What I just listened to was the Prime Minister of the United Kingdom be 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’s a reasonable man who recognises his own hypocrisy if he was to continue along the lines of saying that 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.
“So he has again today outlined that he is not opposed to that second independence referendum, very much building on what he, of course, said in the House of Commons.
“I think this is a very significant moment in Scotland’s constitutional journey.”
The Prime Minister said in the Commons earlier this year that another referendum would only be allowed when the people of Scotland desired it, but he quickly pulled back, again saying another vote was “off limits”.