Scots voted against independence 55% to 45% in a 2014 referendum billed as a once-in-generation poll.
In 2016, the U.K. as a whole voted to leave the EU, but people in Scotland voted strongly to remain.
Sturgeon, who leads the pro-independence Scottish National Party, argues that Brexit changes everything because Scotland should not be dragged out of the 28-nation EU against its will.
The first minister told the Scottish Parliament in Edinburgh that if Britain leaves the EU "a choice between Brexit and a future for Scotland as an independent European nation should be offered in the lifetime of this parliament" - before the next scheduled Scottish election in May 2021.
Sturgeon said the Scottish government would introduce legislation setting the framework for a new referendum. Holding such a vote, however, would need approval from the British government, which right now says the time is not right.
The U.K. government's Scottish Secretary, David Mundell, said Sturgeon "continues to press for divisive constitutional change when it is clear that most people in Scotland do not want another independence referendum."
Sturgeon acknowledged the opposition from the Conservative government in London but said "I believe that position will prove to be unsustainable."
"If we are successful in further growing the support and the demand for independence ... then no U.K. government will be able to stop the will of the people," she said.
Britain's European Union exit, long scheduled to take place last month, has been delayed as Prime Minister Theresa May's government struggles to win Parliament's backing for its EU divorce agreement.
The bloc has given Britain until Oct. 31 to ratify an agreement or leave the 28-nation EU without a deal to smooth the way.
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