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.
Such a referendum would need approval from the British government, which right now says the time is not right.
Sturgeon acknowledged the opposition from the current Conservative-led British government in London but said "I believe that position will prove to be unsustainable."
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