"The Prime Minister's position just now — and it's a position I don't think is sustainable — is that she's not even prepared to have the discussion. And that is putting her at odds not just with me or the independence case. It's putting her at odds with the democratically expressed will of the Scottish Parliament — and that should not be a comfortable place for her to be. I'm pretty certain it's not a sustainable place for her to be," Sturgeon told Sky News.
She highlighted that even in case the United Kingdom managed to secure a free trade deal with the European Union, she would still seek holding a referendum.
"Even the best free trade deal between the UK and the EU is going to be inferior to the position we're in just now, which is full members of the single market," she added.
On Thursday, May said that people should first learn the results of the Brexit talks before asking for another referendum, stressing that it was not the right time for such a vote to be held.
According to the recent poll by Ipsos MORI, half of the Scots would vote for independence if a new referendum took place.
In September 2014, 55 percent of the Scottish people voted against becoming an independent country.