Prime Minister Andy Burnham told John Swinney Scottish independence was “off limits” in a meeting on Thursday, according to the Scottish Secretary.
The pair met in person for the first time on Thursday ahead of the opening ceremony of the Commonwealth Games in Glasgow.
During the meeting, which also included Douglas Alexander and Deputy First Minister Jenny Gilruth, the issue of Scottish independence was raised.
Speaking to BBC Radio Scotland on Friday, Mr Alexander said: “I was alongside Andy as we met John Swinney yesterday in Glasgow and so I can see very clearly how the that conversation progressed and, indeed, what it does mean for Scotland.
The First Minister and Prime Minister met on Thursday (Alastair Grant/PA)PA Wire“Up front, the Prime Minister made clear that independence was off limits.”
He added: “I genuinely believe that we agreed to disagree.
“John Swinney, perfectly honourably, continues to advance the case that he would like to see independence for Scotland – that’s been the cause to which he’s devoted his political life.
“But Andy, in a very reasonable way, was pretty open in saying, ‘listen, respectfully, we’ll agree to disagree on a referendum, and independence is off limits.”
But the First Minister’s push for another vote on independence, the Scottish Secretary said, did not mean the two Governments were unable to work together on other issues.
“Just because we don’t agree on everything doesn’t mean we can’t agree on anything,” he said.
“And, actually, that was a relatively small part of the conversation.”
He added: “There was a very constructive conversation about what, for example, devolution within Scotland could look like.”
Mr Alexander said when he backed the opening of the Scottish Parliament in the 1990s, he had hoped to see powers “pushed out of Holyrood” as well as devolved to it.
Speaking to the Press Association after the meeting on Thursday, Mr Swinney said he knew the Prime Minister did not agree with him on the issue of Scottish independence, but added: “The democratic question has got to be answered.
“I take that view and that is a priority for me to make sure it happens.
“The Prime Minister takes a different view.”