Labour leadership challenger Owen Smith has said he would not oppose another Scottish independence referendum.
The Welsh MP said there should not be another referendum but that it is a matter for the Scottish people.
Mr Smith, who hopes to unseat Jeremy Corbyn, said some of the promises made by the Better Together campaign in 2014 "were contingent on Labour being in power".
He has also called for another referendum on the UK's membership of the European Union (EU) because of the "lies" told by the Leave campaign.
BBC Radio Scotland's Good Morning Scotland programme asked Mr Smith if there should be a rerun of the Scottish referendum.
He said: "No, I don't think so, but the crucial issue we've got to remember is the reason we had a referendum on Scotland is the Tory party.
"There was a Tory Party that had torn itself up over Europe over the previous 20 years.
"We ended up having a vote in Britain largely to satisfy the internal politics of one of our political parties and we now face the prospect of Britain being worse off as a result."
He added: "There are many things that are far more pressing and important than rerunning the referendum in Scotland, on which there was a clear decision just a few months ago."
Asked if he would oppose a second independence referendum, Mr Smith said: "No, of course not.
"If the Scottish people chose that's what they wanted and there was agreement in the Labour Party, then that would be for them to determine it."
He added: "It would be for the SNP to choose to put that to the Scottish people. It's for the Scottish people ultimately to determine what they want."
The BBC presented a list of promises made by the Better Together campaign including continuing EU membership, investment in carbon capture programmes, a secure economy and pensions, and the construction of 13 new Type 23 frigates.
Mr Smith said: "All of those promises were contingent on Labour being in power and Labour isn't in power."
He said Labour would "be able to make good on our promises" if they were in power but fears that Mr Corbyn would leave them in "perpetual opposition".
Mr Smith said there should be a rerun of the EU referendum - in which Scotland voted to Remain and England and Wales voted to Leave - if the Brexit deal leaves the UK worse off.
He said: "If the British people, and the Scottish people, found that they're going to be worse off in the long-term as a result of that decision, they might well choose to change their mind."
He added: "We were lied to, there's no doubt about that.
"We were all told there was an extra £350 million a week for the NHS and there were simple answers to issues around immigration. All of that is completely untrue."