Theresa May has said she is willing to listen to Nicola Sturgeon's options for Scotland to have a different relationship with the European Union.
However, the PM told the people of Scotland they have "had their vote" on independence and this option should not be on the table.
Mrs May met Scotland's First Minister at Bute House in Edinburgh on one of her first engagements since becoming Prime Minister earlier this week.
She said she had "an excellent meeting" with Ms Sturgeon, and looked ahead to more "constructive and positive discussions".
Ms Sturgeon said she received an assurance that the UK Government will be "open and flexible" to options in the forthcoming Brexit process.
Asked if Scotland could have a different relationship with the EU than the rest of the UK, Mrs May said: "I want to get the best possible deal for the United Kingdom out of our negotiations for the UK leaving the EU, but I'm willing to listen to options.
"I've been very clear with the First Minister today that I want the Scottish Government to be fully engaged in our discussions and our considerations, and I will listen to any options that they bring forward."
Asked if she would authorise a second independence referendum, she said: "I think the question is: should there be another referendum?
"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.
"We now have the challenge though, as a United Kingdom, to ensure that we can get the best possible deal for the whole of the United Kingdom from the EU negotiations when the UK leaves the EU.
"I'm very clear that the Government I lead will be for all parts of the United Kingdom and for all people."
Speaking after the meeting, Ms Sturgeon: "I was very pleased that Theresa May said that she was absolutely willing to consider any options that the Scottish Government now bring forward to secure Scotland's relationship with the European Union, and that the process that now takes shape by the UK Government will be open and flexible and that the Scottish Government will be fully involved in that."
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Mrs May said she was keen to visit Scotland so early in her tenure as Prime Minister to demonstrate how "very important" the country is to her.
"When I stood on the steps of 10 Downing Street on Wednesday, I made clear that I believe in the United Kingdom," she said.
"I've just had an excellent meeting with the First Minister - a very constructive and positive meeting.
"We've discussed the upcoming EU negotiations and I'm very clear that I want the Scottish Government to be fully involved and I want to get the best possible deal for the whole of the United Kingdom.
"I've made an early trip to Scotland because Scotland is important to me.
"I wanted to ensure that the first visit I did was up in Scotland."
The European Commission has said it will not hold any Brexit negotiations with any part of the UK until the Prime Minister triggers the formal withdrawal process under Article 50 of the Lisbon Treaty.
The Prime Minister confirmed she had discussed the timescale for triggering Article 50 with Ms Sturgeon.
"Of course we discussed this," she said.
"I've already said that I won't be triggering Article 50 until I think that we have a UK approach and objectives.
"I think it is important that we establish that before we trigger Article 50."
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