Aberconwy MP Guto Bebb, a Wales Office minister, said the Scottish capital had reminded him of Dublin.
The BBC reported that it “should be a warning when visiting a city which is a crucial part of the UK”.
Mr Bebb was in Edinburgh for a British and Irish council meeting.
Mr Bebb said: “We have a huge amount in common with citizens of the Irish Republic, as we do Scotland,” including similar television programmes, popular music and “in many ways a shared literature”.
But he said “read their papers, listen to talk shows and watch the news and it’s clearly another country”.
He said leaving Edinburgh made him feel the same way as he does when leaving Dublin.
“For me Dublin is somewhere which is recognisable but very different.”
“That is fine in the context of the capital of an independent country but it should be a warning when visiting a city which is a crucial part of the UK.
He added: “The sense of nationhood in Edinburgh is palpable. For a long time it has been satisfied within the UK.
“Is that changing though? My gut feeling is yes and that should be a cause for regret to all of us.”