May, addressing the Scottish Conservative Party conference in Glasgow, insisted there would be no benefit to Scotland going it alone when the United Kingdom leaves the European Union.
Uncertainty over Brexit has led to speculation that the Scottish National Party could call for a second independence referendum: in last year's referendum, 62% of voters in Scotland wanted to remain in the European Union.
May accused the SNP, which controls the devolved administration in Edinburgh, of holding an "obsession" with independence and neglecting other domestic issues. She said that a "tunnel-vision nationalism, which focuses only on independence at any cost, sells Scotland short."
She said the UK government would negotiate a deal with the European Union that would protect Scottish interests after Brexit.
"I am determined to ensure that as we leave the EU, we do so as one United Kingdom, which prospers outside the EU as one United Kingdom," May said.
"That means achieving a deal with the EU which works for all parts of the UK -- England, Scotland, Wales and Northern Ireland -- and for the United Kingdom as a whole."
Sturgeon: UK on different path
Scotland's First Minister Nicola Sturgeon has repeatedly argued that Scotland should stay in the European Single Market, even after the rest of the United Kingdom has left.
In a speech Tuesday
, she accused the UK government of ignoring Scotland's views and failing to compromise as it prepares to trigger Article 50, kicking off the formal process of leaving the European Union.
If Scotland doesn't secure a special deal in Britain's negotiations with the European union, Sturgeon said, then "proposing a further decision on independence wouldn't simply be legitimate, it would arguably be a necessary way of giving the people of Scotland a say in our own future direction."
"It would offer Scotland a proper choice on whether or not to be part of a post Brexit UK - a UK that is undoubtedly on a fundamentally different path today than that envisaged in 2014."
In the 2014 Scottish independence referendum
, 55% voted in favor of remaining in the United Kingdom.
The devolved Scottish government published a report in December
which set out ways for Scotland still to maintain its current position in the single market -- which guarantees the free movement of goods, services and people within the bloc -- even if the rest of the UK leaves.
May indicated in a key speech in January
that the UK government will pursue a "hard Brexit," leading to the UK withdrawing from the single market and European customs union.