Theresa May has accused the SNP of having “tunnel vision” over independence as she insisted that “politics is not a game”.
But the prime minister refused to be drawn on whether or not she would grant permission for a second referendum.
She was speaking to BBC Scotland ahead of her speech at the Scottish Conservative conference on Friday.
First Minister Nicola Sturgeon said Mrs May’s government had “no mandate” in Scotland.
And she accused the UK government of “obstinacy and intransigence” in its dealing with the devolved administrations ahead of the formal triggering of the Brexit process, which is expected to happen later this month.
The Scottish government has published a 60-page document which sets out proposals it believes could allow Scotland to remain in the EU single market even if the rest of the UK leaves – with Ms Sturgeon saying a second independence referendum is “all but inevitable” if that does not happen.
Mrs May said she was “looking very closely” at the proposals, adding: “We are working with them on those plans – there are issues that they have raised that we have taken on board.”
She said her objective was to use the Brexit negotiations to secure a “good trade agreement that works for the whole of the UK, but crucially a trade agreement that works for Scotland as well.”
And she said it was wrong to say she backed a so-called “hard Brexit”, but that she instead wanted “a Brexit that is going to be right for the United Kingdom, and that means being right for all parts of the United Kingdom”.
She also said it was “very clear” that people in Scotland did not want another vote on independence – but did not say whether she would grant permission if the Scottish Parliament called for a second referendum.
Mrs May added: “To me, politics isn’t a game. Politics is about people’s lives, it’s about delivering on the issues that really matter to them on a day-to-day basis.
“I can’t help but feel that the SNP has a tunnel vision about independence. Actually I think what people want is for the SNP government to get on with dealing with the issues they want to see addressed on a day-to-day basis.
“Issues like the state of the economy, reforming schools – education used to be such a great flagship for Scotland, but sadly in recent years we have seen that deteriorating.”
Mrs May said she was “passionate” about preserving the United Kingdom – which she described as the most successful political union in history – and pointed out that the first visit she had made as prime minister was to Scotland.
In a speech earlier this week, Ms Sturgeon warned that elements of farming and fishing policy could be taken back to Westminster after Brexit, despite promises by the Leave campaign that they would be handed to Holyrood.
And she said devolution was facing a “grave challenge” after “20 years of progress”.
But Mrs May said “no powers that are currently there will be taken away, but more could come” to the Scottish Parliament after Brexit.
She added: “There will be some areas where we do need to ensure there is a UK framework to make sure that this very important single market of the United Kingdom, which matters so much to Scotland, is working properly.
“But what we are talking to all of the devolved administrations about is when we bring powers back from Brussels, what should stay at a UK level and what should be further devolved?”
In response, Ms Sturgeon said the Scottish government had offered “substantial concessions” over Brexit in its dealings with the UK government, which she said had shown “no similar willingness to compromise but has in fact hardened its position over Brexit”.
She added: “If the prime minister thinks she can come to Scotland and sermonise about where power should lie, in the manner of one of her Tory predecessors, she should remember this: Her government has no mandate in Scotland, and no democratic basis to take us out of Europe and the single market against our will.
“But increasingly, this Tory government seems to think it can do what it wants to Scotland and get away with it.”
In her speech at the two-day Scottish Conservative conference in Glasgow, Mrs May will highlight her commitment to “strengthening and sustaining the bonds that unite us” and say she is confident about the future of the UK.
She will also praise the work done by Scottish Conservative leader Ruth Davidson, who she will say has successfully “exposed the SNP’s mismanagement of Scotland’s schools”.
The Conservatives are currently the second-largest party in the Scottish Parliament, having overtaken Labour in last year’s election.
Theresa May: SNP has independence ‘tunnel vision’}