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Speaking in Edinburgh, Mrs May said: I have already said that I wont be triggering Article 50 until I think that we have a U.K. approach and objectives for negotiations. I think it is important that we establish that before we trigger Article 50.
Ms Sturgeon has promised to explore every option to keep Scotland in the EU, and has repeatedly warned that if that is not possible as part of the UK, it is highly likely to lead to a second independence vote.
The Prime Minister said: "As far as I'm concerned the Scottish people had their vote, they voted in 2014, and a very clear message came through, both the United Kingdom and the Scottish Government said they would abide by that.
Speaking before the meeting, only the third between the pair, she said her visit to Scotland demonstrated her commitment to "preserving this special union that has endured for centuries.
Ms Sturgeon said afterwards that she had received an assurance that the UK Government would be "open and flexible" to options in the forthcoming Brexit process.