The First Minister admitted she has been left “frustrated” by the approach of the Tory leader since they met in Edinburgh in the days after Mrs May replaced David Cameron in Downing Street.
The SNP leader warned again that Scotland must be allowed to stay in the EU single market even if other parts of the UK leave – and that failure to secure this will mean a second independence referendum is staged.
Ms Sturgeon again repeated her belief that such a scenario is now “highly likely” in the aftermath of the Brexit vote.
Proposals for a separate deal which Scotland could broker with the EU will be published by Ms Sturgeon in the next few weeks, while a new Bill for a second independence referendum will be unveiled in the coming days.
Ms Sturgeon said: “Theresa May, perfectly legitimately, has said she values the UK, she wants to keep the UK together. In the independence referendum, Scotland was told repeatedly it was an equal partner in the UK.
“My message to the Prime Minister is, it’s now time to prove these things and demonstrate to Scotland that our voice does count in the UK and our interests can be protected. If that’s not the case, then I think Scotland would have the right to decide whether it wanted to follow a different path.”
Scotland voted 62 per cent to 38 per cent in favour of remaining in the European Union in the June referendum, but the weight of votes south of the Border swung the result in favour of Leave.
Ms Sturgeon admitted yesterday she is fed up being frozen out of the Brexit proposals by the new Prime Minister.
“I think it has been frustrating, if I can be diplomatic about it,” Ms Sturgeon said yesterday. “Theresa May came to Edinburgh just a couple of days after she became Prime Minister, gave a commitment to me and to Scotland that we’d be fully involved and that she would listen to options we put forward.
“I think it’s fair to say that promise hasn’t yet been fully honoured and I hope we’ll see it honoured in the days to come.”
The First Minister said it would be “challenging” but “possible” for Scotland to remain in the single market outside the EU, even if the rest of the UK is not party to such an arrangement. She told the SNP conference last week that detailed proposals will be published within weeks.
“We are going to put forward proposals, that we would hope that the UK government would be prepared to listen to, that would allow Scotland to preserve its place in the single market and preserve aspects of its relationship with the EU,” Ms Sturgeon said.
“What I’m trying to do is to explore options whereby Scotland doesn’t have to leave the European Union or the single market, because we voted to stay in.”
The First Minister is due meet the Prime Minister along with the leaders of other devolved administrations next Monday at the first meeting of the Joint Ministerial Committee to discuss Brexit.
The SNP leader has also said that the UK government’s current reluctance to share its negotiating position on Brexit with the public or the House of Commons is “unacceptable”.
Ms Sturgeon said: “The House of Commons and the wider public has almost been told to butt out and mind their own business, and we saw in the House of Commons last week there’s not a lot of support for that kind of approach.”
She said it was not acceptable to have a “secret negotiating strategy” and it should be shared with the public and endorsed by parliament.
At last week’s SNP conference, the First Minister pledged that the Scottish Government will call a second independence referendum if the UK opts for a “hard Brexit”, but said she wants to work with others to try and “save” the UK from being removed from the single market.
The Scottish Government’s draft independence referendum bill will be published for consultation next week. The SNP has already launched a campaign to reach out to those who voted No in 2014 but who are now wavering.
But Scottish Secretary David Mundell played down claims that the EU result in Scotland was grounds for another vote on leaving the UK.
He said: “We’ve had a vote which we were told was a once in a generation vote as to whether Scotland should remain part of the United Kingdom – there was a decisive result in that vote.
“We were aware there was going to be a vote on whether the United Kingdom remained in the EU. The reasons for Scotland remaining in the UK were overwhelmingly economic and those are the same issues that there was today in relation to the UK single market.
“I find it very odd that people who are very, very concerned about the EU single market are quite willing to give up the UK single market, which is four times as valuable to Scotland and responsible for a million jobs.”
The UK government would have to authorise a new referendum on Scottish independence if it was to be legally binding because constitutional issues are reserved to Westminster, but Mr Mundell refused to explicitly state whether it would or not.
“There could be another referendum, but we want to argue that there shouldn’t be another referendum.
“I’ve said from the outset that we would listen to any proposals that the Scottish Government brought forward in relation to Scotland’s interests.
“We’ve had four months and no specific proposals have come forward.
“I see it as impossible, for example, that Scotland could remain in the EU while the rest of the EU left.”
Asked whether Scotland could stay in the single market, Mr Mundell said: “I think it’s difficult to see how that would be achieved, but I’ve said before we will listen to any proposals that the Scottish Government brings forward.”