Sturgeon however did want to elaborate on what she would do if London blocked Scotland from holding a second referendum.
The Prime Minister told MPs it was "not a moment to play politics or create uncertainty" and accused the Scottish National Party of "constitutional game playing".
She spoke following First Minister Nicola Sturgeon's announcement today that the Scottish Government is seeking approval from Holyrood on a referendum on Scottish independence.
The SNP won the Scottish Parliament elections past year on a manifesto that explicitly said another referendum was an option if Scotland was "taken out of the European Union against our will".
In a 2014 referendum, Scottish voters rejected independence by a margin of 55 percent to 45 percent.
The SNP leader warned that another referendum was "highly likely" in the immediate aftermath of the Brexit vote, which saw 62 per cent of Scots vote to Remain.
She said she was open to discussions with the Prime Minister but the response of the UK Government so far shows they are "not willing to compromise".
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Ms Sturgeon said she hoped Scotland would be able to stay in the European single market and customs union, but has become convinced Ms May is pursuing a "hard Brexit" that would leave Britain on its own.
"I am ensuring Scotland's future will not just be decided by me, but the people of Scotland".
Scotland's parliament has a pro-independence majority, and the Scottish government has published proposals outlining how Scotland could remain in the European Union, even after the United Kingdom leaves.
But Nicola Sturgeon said she wants another independence vote as early as next year.
According to the head of the regional executive, London's plans to pull the United Kingdom out of the European single market in order to control immigration, the process which is called Brexit, 'will damage the economy and change the nature of our society and country'.
On being asked about the tentative date for next referendum, Sturgeon said it could be held between autumn of 2018 and spring of 2019. Theresa May has also confirmed that she will take Britain out of the single market - one of the "red lines" previously set by Ms Sturgeon for another vote.