The UK Government turned down the EC's offer of a legal opinion on Scotland's status in Europe, saying it would not "pre-negotiate" the terms of an independence settlement.
But in a surprise move, the Scottish Government, which has faced days of criticism over its claim that EU membership would be automatic following a vote for independence, accepted the decision, claiming it was "a matter for the UK Government".
The refusal to take up the EC's offer means voters will be denied a potentially significant – though not definitive – view of the terms under which Scotland might join the EU before the referendum in 2014.
Scottish Labour hit out at the impasse and called for the EC to be consulted.
In a statement, a UK Government spokesman said: "We are clear we are not pre-negotiating the terms of separation from the UK ahead of the referendum.
"It is the Scottish Government's policy on independence which is causing this uncertainty and they should be prepared to deal with the many questions it raises. This Government has confirmed it does hold legal advice on this issue.
"Based on the overwhelming weight of international precedent it is the Government's view that the remainder of the UK would continue to exercise the UK's existing international rights and obligations and Scotland would form a new state."
A spokesman for First Minister Alex Salmond confirmed the Scottish Government was not challenging the UK Government's decision.
He said: "This is a matter for the UK Government. We will consider our options in this matter as we move forward.
"The European Commission have offered to provide legal opinion on an independent Scotland's continuing membership of the EU to the UK Government, as the relevant member state – an offer it has so far declined to take up."
The European Commission offered to provide a legal opinion on an independent Scotland's membership of the EU in the wake of the Edinburgh Agreement establishing the framework for the referendum. The move follows comments by EC President Jose Manuel Barroso and Vice-President Viviane Reding suggesting an independent Scotland would have to apply for membership.
The Scottish Government maintains membership would be automatic and that Scotland would continue in the EU on the same terms as the UK.
Patricia Ferguson, Scottish Labour's constitutional spokeswoman, called for ministers in London and Edinburgh to push for clarity from the EC. She said: "We think the UK Government should ask the EU Commission for a legal opinion on Scotland's potential status post-separation. Alex Salmond should ask the UK Government to do this; and we will support the First Minister."
Scottish LibDem leader Willie Rennie said: "I agree with the UK Government it is not for them to negotiate Scottish independence as it's a policy they do not support. However, it is curious the SNP, a party never shy to demand action from the UK Government, is so quiet now."
The stand-off came as questions over EU membership again dominated First Ministers Questions at Holyrood. Scots Labour leader Johann Lamont said Mr Salmond was "treating the people of Scotland like fools" over claims on EU membership.
The First Minister insisted an independent Scotland would be "welcomed with open arms" by the EU.