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Theresa May underlined the importance of keeping Britain united by making her first official visit to Scotland.
The Prime Minister met First Minister Nicola Sturgeon, and said she will listen to options to satisfy Scotland's wish of keeping close ties with Europe.
ITV News' Deputy Political Editor Chris Ship reports:
Scottish First Minister Nicola Sturgeon has said she is determined to consider all options to protect Scotland's relationship with the EU.
Ms Sturgeon said her meeting with British Prime Minister Theresa May on Friday was "constructive", adding that she was pleased Mrs May was willing to consider options raised by Scotland.
"It was very important today to get a commitment from the prime minister...to listen to options that the Scottish government brings forward," Ms Sturgeon said.
"There is an agreement that Scottish government officials will be very closely involved in discussions."
Ms Sturgeon said Scotland may have to consider becoming independent in order to protect its with membership of the EU, but insisted she would "consider all the options along the way".
The prime minister knows, as everybody else knows, that a second independence referendum is of course on the table because Scotland finds itself now in the position of facing exit from the EU against our will.
Article 50 will not be brought forward until there is a UK-wide approach, Theresa May has said.
Speaking after meeting with Scottish First Minister Nicola Sturgeon, Mrs May said: "I'm willing to listen to options and I've been very clear with the first minister today that I want the Scottish government to be fully engaged in our discussions.
"I have already said that I won't be triggering Article 50 until I think that we have a UK approach and objectives for negotiations - I think it is important that we establish that before we trigger Article 50."
The newly appointment British prime minister has used her "Brexit is Brexit" mantra to reassure the majority of the British public who voted to leave the EU that she is serious about negotiating Britain's exit from the bloc.
Theresa May greeted Scotland's First Minister Nicola Sturgeon as she arrived in Edinburgh on Friday.
The prime minister is to hold a meeting with Sturgeon to show her commitment to preserving the "special union" of the UK, she said ahead of her visit.
Last month, Mrs Sturgeon said a second independence referendum was "highly likely" after the UK voted to leave the European Union.
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Nicola Sturgeon said it is her "intention" to "secure continued access to the single market for Scotland" following Brexit.
The First Minister is set to travel to Brussels on Wednesday to set out Scotland's interests with EU officials.
Speaking in the Scottish Parliament on Tuesday, she said the result of the EU referendum had left her "deeply disappointed" and "profoundly concerned", but is "utterly determined" to "protect Scotland's relationship with and our place in the European Union".
Ms Sturgeon added that she is "committed" to "listening, understanding and seeking to address the concerns" of those in Scotland who voted to leave the EU.
The First Minister said action must be taken to ensure "the will of Scottish people" is respected, after the country voted in favour of remaining in the European Union.
Scotland's First Minister Nicola Sturgeon is to meet European Parliament President Martin Schulz in Brussels on Wednesday, a source told Reuters.
The meeting follows last week's referendum on Britain's membership of the EU, in which a majority of Scotland's population voted to remain in the bloc despite the leave campaign's victory.
Ms Sturgeon has said she will pursue all available options to keep Scotland in the EU, and that a second referendum on Scottish independence from the UK is "highly likely".
There will be a special motion in Scotland's devolved parliament on Tuesday, which will aim to give the Scottish government backing for discussions on options to protect Scotland's relationship with the EU.