Video report by ITV News Political Editor Robert Peston
Theresa May has ruled out the possibility of a second Scottish independence referendum in 2018 or 2019.
First Minister Nicola Sturgeon said the prime minister's announcement could turn today into "the day the fate of the union was sealed".
Mrs Sturgeon wants a second vote on pulling Scotland out of the UK as soon as next autumn, with the Scottish parliament set to vote on the matter next Wednesday.
But speaking to ITV News Political Editor Robert Peston, the prime minister dismissed the notion, repeatedly saying: "Now is not the time."
In the interview, Mrs May also:
said she had "absolute faith" in Chancellor Philip Hammond after the National Insurance contributions U-turn
reacted to the Electoral Commission's decision to fine the Conservatives £70,000 for election campaign expense "failings"
Mrs May accused the SNP of jeopardising the UK's negotiations with the EU with talk of a second referendum.
She said asking people in Scotland to make such a "crucial" decision without knowing what the EU deal will be would be "unfair".
Mrs Sturgeon said the Conservative government's stance was like "winding the clock back to the bad old days of Margaret Thatcher".
"It is an argument for independence really in a nutshell," she said.
Video report by ITV News Correspondent Martin Geissler
"Westminster thinks it has got the democratically elected mandate of the Scottish Government and the majority in the Scottish Parliament.
"History may look back on today and see it as the day the fate of the union was sealed."
Mrs May had said "working together" was the best chance for Scotland and for the rest of the UK to get the best deal in the wake of the Brexit vote.
"We should be working together, not pulling apart," she said. "Now is not the time. This union we have is very precious.
"We've been joined together for over 300 years. We've had a great history together - I believe we have a great future together.
"Together, we should put our energies into making sure we get the right deal for Scotland and for the whole of the UK."
The first minister earlier responded to Mrs May's statement in a series of tweets, saying she was not proposing a referendum "now" but rather when the terms of Brexit are clear.
A spokesman for the first minister meanwhile described Mrs May's statement as "spectacularly unclear".
He said: "If we do get clarity that what the PM means is that discussion about a referendum should not even begin until some point after Brexit, then effectively what the PM is doing is unilaterally blocking a referendum. That would be a democratic outrage."
Asked how badly such a move would go down in Scotland, he said: "I think it would play disastrously. I think it would be a miscalculation and a blunder of epic and historic proportions".
Scottish Secretary David Mundell also entered the row, saying the UK government would not enter into "discussions or negotiations" on a request for the legal power to hold a vote, adding: "This argument isn't about mandates."
The prime minister was also asked by ITV News about the U-turn following last week's budget speech by Chancellor Philip Hammond.
She said she had "absolute faith" in Mr Hammond and never considered asking him to resign after the government backtracked on a manifesto-breaking promise not to increase National Insurance contributions (NICs).
Mrs May said while she believed the proposed NICs increase for self-employed was the right plan, she and the chancellor both "recognised the spirit of the manifesto".
She denied either the NICs U-turn or the Conservatives' expenses "failings" fine would be harmful to public trust in politicians.
"You talk about trust in politicians from the British people - this has been an important week," she said.
"If you look at what happened at the beginning of this week, Parliament passed the legislation which enables us to invoke Article 50.
"I believe it is absolutely right. What the British people have said to us is 'we voted last year, we want to leave the European Union, and we want you to deliver on that. We trust you to deliver' - and that's what we will be doing."