In another interview with ITV, May declined to confirm whether she would always block a Scottish independence referendum, or whether her stance only applied up to the end of the Brexit negotiations, projected to come in 2019.
Sturgeon said Scotland should have the chance to stay in the EU's lucrative single market and keep an open-door policy to immigrants after voting to remain, and has criticised May for failing to consult the Scottish government on her strategy.
However, the prime minister today told Sturgeon that "now is not the time" to hold a referendum as it would "not be fair" to expect the Scottish people to vote again when the UK's future relationship with European Union is still unclear.
She told the Channel 4: 'If we don't have the option of a referendum then effectively we are accepting right now a future that is a hard Brexit future with Conservative governments at Westminster for perhaps 20 years or more.
But May said earlier that the Tories would not allow any discussion of the referendum until the UK's Brexit deal had been signed and Scottish voters had time to weigh it up, implying any referendum may not happen until 2021 at the earliest.
The First Minister responded on Twitter saying she was not proposing a Scottish referendum now but when the terms of Brexit (were) clear.
She said: "More than that I think it wouldn't be fair to the people of Scotland because they'd be asked to make a crucial decision without the necessary information, without knowing what the future partnership will be or what the alternative for an independent Scotland would look like".
Ruth Davidson, the Scottish Tory leader, and David Mundell, the United Kingdom government's Scottish secretary, were forced to deny that May had been persuaded to make her statement on the eve of the SNP conference to provoke its activists into taking a far more partisan stance.
"If this Government are thinking for one minute of standing in the way of Scottish democracy, it will be the biggest recruiting sergeant possible for the cause of Scottish independence".
The Scottish first minister hit back, branding Mrs May "undemocratic", amid fury from other nationalists.
Mrs May had earlier said that her message to Ms Sturgeon on a referendum was clear - "now is not the time".
We have found ourselves in this situation because of the Tories' failure to respond to Scotland's overwhelming vote to remain in the European Union, or the subsequent efforts of the Scottish Government to find a compromise.
There has been talk of special deals for the auto industry and others, but a point blank refusal to discuss in any meaningful way a differential approach for Scotland and what Scotland deserves in light of the material change of circumstances brought about by the Brexit vote.
It comes after May clashed with Sturgeon over the potential for a new independence referendum.