In an article for The Times, Theresa May tackles claims that her approach has made a second independence vote more likely.
She writes that she does not believe that Scotland’s majority support for the EU represents a wish for independence.
In her article she appeals to Scots, 62 per cent of whom voted to remain in the bloc, by saying that her Brexit plan addresses concerns raised in Scotland as well as the rest of the UK.
She says that the UK and the EU will remain “strong allies” and form “a strategic partnership” involving a free trade arrangement.
And she stresses her intention to protect both workers’ rights and the rights of EU citizens in Scotland.
She commits to Scottish universities and research and says that her government wants to continue to collaborate with Europe on programmes.
On the issue of the single market, she says that, while there will not be membership, there will be “the freest possible trade in goods and services between the UK and EU states”.
“We want to take in elements of current single market arrangements in certain areas — for example, the freedom to provide financial services, an important sector in the Scottish economy,” she writes.
Her comments come after a major speech this week in which the Prime Minister rejected the possibility of retaining single market membership.
The speech has prompted Scottish First Minister Nicola Sturgeon to say that a second referendum is now “all but inevitable”.
But the prime minister has claimed Scottish businesses place greater importance on the UK single market.
She calls for a Team UK approach in negotiations and says: “Our guiding principle must be to ensure that no barriers to living and doing business within our own union are created.”
Mrs May visited Bute House two days after becoming prime minister to pledge to work closely with Ms Sturgeon’s government.
She has since been criticised for failing to engage.
However, the prime minister says her commitment to the SNP’s engagement in the Brexit process “remains absolute”.
Mrs May’s article comes as she prepares to address the World Economic Forum in Davos, Switzerland.
She is expected to tell leaders that the UK is “open for business” but will also warn about those “left behind” by globalisation.
Her Times article also comes after European leaders on Wednesday criticised Boris Johnson for comparing the French president to a Second World War guard administering “punishment beatings”.
The foreign secretary had been asked about reported remarks from an aide to François Hollande, claiming that Britain could not expect a better trading relationship with Europe outside the EU.
“If Monsieur Hollande wants to administer punishment beatings to anyone who chooses to escape, rather in the manner of some World War Two movie, then I don’t think that’s the way forward,” Mr Johnson said in Delhi.