Sir Michael said the Conservatives at Westminster would not grant the First Minister the power to hold another independence ballot, as he instead urged her to “get to grips” with problems in Scotland’s schools, health service and economy.
When asked if the UK Government would facilitate another referendum in this Parliament, Sir Michael told the Herald : “No, forget it. The respect agenda is two-way.
“She (the First Minister) is constantly asking us to respect the SNP Government but she has to respect the decision of Scotland to stay inside the UK in 2014 and the decision of the UK to leave the EU.
“Respect works two ways.”
Ms Sturgeon accused him of “backpedalling” on the issue when during a radio interview he later refused to say if Westminster would block a second independence referendum.
Pressed on BBC Radio Scotland’s Good Morning Scotland programme, the Defence Secretary said: “We don’t see the need for a referendum, I think this is a diversion.
“What the Scottish Government should be focusing on is what it was elected to do, which is improve school standards, get to grips with the problems in Scottish hospitals, and reverse the serious rise in unemployment.”
Ms Sturgeon raised the prospect of another referendum after Scotland voted to stay in the European Union but the UK as a whole voted to leave.
She has also said Prime Minister Theresa May’s intention to take the UK out of the European single market “undoubtedly” increases the chances of a second vote.
Sir Michael said: “Scotland voted in a UK referendum and overall the United Kingdom voted to leave.”
Criticising Ms Sturgeon, he said: “She is trying to divert attention from her failure at the moment to get to grips with the main issues that affect Scotland - that is not a referendum.
“What people in Scotland want to know is do they have a Government that is prepared to deal with the challenges in Scotland, particularly in schools and hospitals and also in the economy. Anything else is a diversion.
“We’ve made it clear there is no need for a second referendum and the Scottish Government should be getting on and dealing with the things the Scottish Government was elected to deal with.”
Reacting to his remarks, a spokesman for Ms Sturgeon said: “The arrogance of the Tories knows no bounds. They now think they can do what they want to Scotland and get away with it – not content with trying to drag us out of EU against our will with the support of just one MP out of 59 in Scotland, they are now suggesting they might try to block the nation’s right to choose a different path.
“Any Tory bid to block a referendum would be a democratic outrage, but would only succeed in boosting support for both a referendum and for independence itself – something which the Prime Minister has previously indicated she understands all too well.
“Our mandate is unequivocal, with a manifesto commitment which makes explicitly clear that the Scottish Parliament should have the right to decide on an independence referendum if Scotland faces being taken out of the EU against our will. And no Tory Westminster government has a right to stand in the way of that.
“Michael Fallon’s comments betray how rattled the Tories are about Scotland – but his frantic backpedalling when pressed on the issue this morning shows that he understands what a disastrous strategy it would be for them to try and deny Scotland’s democratic right.”