The Chancellor of the Duchy said the government would “absolutely” not hold another public poll on the matter, regardless of how Scotland votes in the 2021 Holyrood election.
But the Scottish First Minister accused the Tories of “raging against reality” by blocking another independence vote and vowed to “pursue the plan I won a mandate for”.
It marks the latest affront in a growing gulf between Westminster and Holyrood even before the new British parliament is officially opened.
Ms Sturgeon, whose Scottish National Party won 48 of 59 seats in Scotland on Thursday night while the Scottish Conservatives fell from 13 to six MPs, warned Scotland “cannot be imprisoned in the Union against its will”.
Mr Gove told Sky’s Sophy Ridge on Sunday: “We were told in 2014 that would be a choice for a generation, we are not going to have an independence referendum on Scotland”.
With the Tories having won Labour voters across the North of England and the Midlands, Mr Gove stressed the need to deliver for its new supporters.
“We need to make sure that economic opportunity is more equally spread across the country.”
He also claimed the next phase of Brexit negotiations will be concluded by the end of 2020.
“Quite a lot of the details that we need to negotiate is already laid out in the political declaration, so a lot of work has been done,” he said, adding he is “confident” of the UK departing on January 31 and sealing a trade deal “in short order”.
He said he would not get into “speculation” about whether the Withdrawal Agreement Bill will be brought back to the Commons before Christmas, but said it would be voted on in “relatively short order” ahead of the January deadline.
But as Boris Johnson feels vindicated by his landslide majority of 80 to pursue his Brexit approach, Ms Sturgeon is adamant that she too commands a mandate for a Scottish vote in the second half of 2020.
She confirmed that she will “set out this week the detailed, democratic, case for the transfer of power” to Holyrood to allow for a legal referendum to take place.
“If he thinks – and I said this to him on Friday night on the telephone – that saying no is the end of the matter, he is going to find himself completely and utterly wrong,” she told the BBC’s Andrew Marr on Sunday morning.
“If the United Kingdom is to continue, it can only be by consent and if Boris Johnson is confident in the case for the Union he should be confident enough to make that case and allow people to decide.”
Mr Johnson spoke to Ms Sturgeon on the phone after returning to Number 10, saying he “remains opposed” to a second Scottish poll.
A Downing Street spokesman said the prime minister was “standing with the majority of people in Scotland who do not want to return to division and uncertainty”.
Additional reporting by PA Media.
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