Scottish Secretary David Mundell said it would not enter into "discussions or negotiations" on a request for the legal power to hold a vote.
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Mr Mundell said: "This argument isn't about mandates, it's about holding a referendum on established criteria which were set on in the Edinburgh Agreement.
"That established that a referendum must be legal, fair and decisive.
"The proposal brought forward is not fair, people will not be able to make an informed choice.
"Neither is there public or political support for such a referendum.
"Therefore we will not be entering into discussions or negotiations about a section 30 agreement and any request at this time will be declined."
First Minister Nicola Sturgeon has said she wants a new vote before a deal on Britain's withdrawal from the European Union is finalised.
She has said she does not want a referendum now, but when the terms of Brexit are clear and ''before it is too late to choose an alternative path''.
Speaking alongside Mr Mundell at a press conference in Edinburgh, Scottish Conservative leader Ruth Davidson said: "We reject conclusively the timetable for a referendum set out by the Scottish Government for a key reason - because it is unfair to Scottish voters.
"We've just come through a referendum campaign where a key complaint among many people was that they did not have the necessary information to help them make an informed decision.
"If we were to keep to the First Minister's timetable this is exactly what would happen in Scotland too. On the most important political decision a country can make we would be voting blind.
"I believe that it's only right that people should have the opportunity to examine the UK's new relationship with the European Union once it is up and running.
"People should only be asked to make a judgment on whether to leave or remain within a 300-year-old union of nations when they have seen for themselves how that union is functioning following Brexit.
"They should also know what the alternative entails and we have seen no clarity from the SNP on even the basic questions of their proposition."
Mrs May told ITV News's Robert Peston: ''Right now we should be working together, not pulling apart.
''We should be working together to get that right deal for Scotland, that right deal for the UK, as I say that's my job as Prime Minister and so for that reason I say to the SNP: now is not the time.''
The Prime Minister said the focus of the entire UK should be on the forthcoming Brexit negotiations.
She said a new vote on Scottish independence would make it more difficult to get a ''good deal'' with the remaining 27 member states.
''So when the SNP Government say that it's the time to start talking about a second independence referendum, I say that just at this point all our energies should be focused on our negotiations with the European Union about our future relationship,'' she said.
''And to be talking about an independence referendum will, I think, make it more difficult for us to be able to get the right deal for Scotland, and the right deal for the UK.
''More than that I think it wouldn't be fair to the people of Scotland because they'd be asked to make a crucial decision without the necessary information, without knowing what the future partnership will be or what the alternative for an independent Scotland would look like."
MSPs will vote next Wednesday on whether they will support Ms Sturgeon's request for a section 30 order from Westminster, which would be needed for Holyrood to hold a legally binding ballot.
Responding to the interview, Ms Sturgeon said she does not want a referendum now, but when the terms of Brexit are clear and ''before it is too late to choose an alternative path''.
On Twitter, she added: ''If the Tories refuse to do so, they would effectively be blocking Scotland's right to choose when the Brexit terms (are) clear.
''This would be undemocratic given @scotgov (the Scottish Government's) clear mandate and also proof positive that the Tories fear the verdict of the Scottish people.''
The support of the pro-independence Scottish Greens will give the SNP the majority it needs in the Scottish Parliament to request a Section 30 order.
The party's external affairs spokesman, Ross Greer MSP, said: "If a Tory Westminster Government that Scotland did not elect seriously think they can block our right to choose - and that they can veto a decision of our elected parliament - they will only increase support for independence. Today's comments underline the contemptuous attitude the Tories have toward Scotland."
But Scottish Labour leader Kezia Dugdale said: "There absolutely should not be another independence referendum until after Brexit.
"We have no idea what Brexit looks like, or how it will impact our economy and families in Scotland. People cannot be asked to make a decision about the future of our 300-year-old Union in the dark.
"If there is to be another vote, the people of Scotland deserve clarity on what they are being asked to vote on."
Scottish Liberal Democrat leader Willie Rennie MSP said: "Scottish Liberal Democrats are opposed to a divisive second referendum. Our opposition was in our manifesto for the Holyrood election last year and we will stick to that.
"It is not the right time, there is not public demand for one and there is not a proper mandate for one."