The Prime Minister insisted she will deliver on quitting the EU and made clear Holyrood will not get a decisive role in divorce talks.
Throwing down the gauntlet to the First Minister over threats of another independence referendum, Theresa May called for "certainty and leadership" to embrace the "opportunities ahead."
The Prime Minister will chair a meeting of the Joint Ministerial Committee with Ms Sturgeon and other devolved administration leaders in Cardiff.
Theresa May had to remind Nicola Sturgeon that the EU referendum voted in favour of Brexit
The Supreme Court last week rejected her argument that Holyrood should have a say on the triggering of Article 50.
But she still plans to bring forward a "legislative consent motion".
SNP MPs will also attempt to stall Brexit with 50 amendments to the crucial EU (Notification of Withdrawal) Bill, that comes to Commons tomorrow for its first debate.
The Supreme Court ruled Scotland does not have to be consulted on Article 50 matters
Today's JMC meeting is the second Mrs May has chaired personally and the first ever held outside London.
The UK voted to leave the EU, and the UK Government has a responsibility to deliver on that mandate
It will focus on Britain's exit from the EU and how the four nations of the UK can work together to help firms trade and invest.
Speaking ahead of talks, Mrs May said the full engagement she had promised the devolved administrations was happening and she hoped for "further constructive discussions".
But she stressed: "We have also had the Supreme Court judgement which made clear beyond doubt that relations with the EU are a matter for the UK Government and UK Parliament.
Government Loses Brexit Vote Appeal
Tue, January 24, 2017
Britain's most senior judges ruled that Prime Minister Theresa May does not have the power to trigger the formal process Article 50 for the UK's exit from the European Union without Parliament having a say.
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Issued by the Supreme Court of (top row, from the left) Lord Neuberger, Lord Mance, Lord Kerr, Lord Sumption, (bottom row, from the left) Lady Hale, Lord Clarke, Lord Wilson and Lord Hodge, who agreed with the majority decision that the Government could not trigger Article 50 without Parliamentary approval.
"We should not forget that that means MPs representing every community in the UK will be fully involved in the passage of Article 50 through Parliament.
"The UK voted to leave the EU, and the UK Government has a responsibility to deliver on that mandate and secure the right deal for the whole of the UK.
"We all have a part to play in providing certainty and leadership so that together we can make a success of the opportunities ahead."
But Ms Sturgeon claimed time was running out for Mrs May to "heed the voice of Scotland", with 62 per cent of voters north of the Border backing Remain in last June's poll.
Mrs May reminded that the Government has a responsibility to trigger Brexit
She insisted her plan to keep Scotland in the EU single market even if the UK leaves and calls for more Holyrood more powers over immigration represented "significant compromises".
She said: "It is becoming clearer with every day that passes that the UK Government is determined to pursue a hard Brexit and I am determined to do all I can to protect Scotland's from the devastating impact that would have.
"Time is running out for the Prime Minister to demonstrate that she is going to uphold the commitment she made to me shortly after taking office that Scotland will be fully involved in discussions to develop an agreed UK approach and listen to alternative proposals for Scotland."