Theresa May said now was "not the time" for a referendum - but did not say when the correct time would be. Ms Sturgeon said blocking a referendum would be a "democratic outrage". But May has ruled out a referendum while Brexit negotiations with Brussels are taking place.
The SNP and Scottish Greens support giving the people the right to decide the country's future in light of the new found Tory ascendency at Westminster and the chaos of a Tory Hard Brexit and exit from the single market.
She was pressed on whether that would apply if a referendum was consultative, not legally binding, and added: "I t's a slightly different constitutional situation, but the basic principle holds".
MSPs in Holyrood are poised to endorse the call for a second referendum next week but it is set to go ignored in Westminster.
The Conservative leader has already shot down Sturgeon's call for a referendum between autumn 2018 and spring 2019 once, stating that "now is not the time", but May is expected to land that aspiration a further blow.
The Prime Minister insists the country must focus first on securing the best possible Brexit deal - the event Ms Sturgeon says justifies reopening the question.
Mundell said there would be no negotiations on Section 30, a procedure that allows the Scottish parliament to legislate for an independence referendum. If it does, that is what I will do.
On Monday, following the United Kingdom parliament's decision to allow the British government to invoke Article 50 and initiate talks on post-Brexit ties with the European Union, Scottish First Minister Nicola Sturgeon said that she would seek the authority to hold another independence referendum, which should take place between fall 2018 and spring 2019 to accommodate for Brexit negotiations.
"It would be outrageous for the Scottish Parliament to be frozen out of the process".
"Right now we should be working together, not pulling apart", May said in a televised interview. The SNP argue we must break up the United Kingdom because we are leaving the EU.
Sturgeon will seek approval in the Scottish Parliament in Edinburgh for a new vote next Wednesday, but London has the right to block the request.
She told delegates: "We've seen that tunnel vision on display again this week".
Speaking about the Prime Minister, he added: " This is potentially productive for her politically, even though it's high stakes, it may well be helpful for her politically, and it's important to remember that".
May had previously said there was no appetite for a second referendum less than three years after Scots voted by 55% to 45% to reject independence, in September 2014.
The SNP's Europe spokesperson Stephen Gethins MP, when asked if he fears EU nationals might be disenfranchised, said: "You can understand why there's significant concerns by European nationals who have made Scotland their home". "A plan to make the most of the opportunities ahead and to build a stronger, fairer Britain that is more united and more outward-looking".