She said she will seek powers to hold a second vote because of her desire to keep Scotland in the European bloc.
The popular leader said she was keeping a promise made by the Scottish National Party to consider a second independence vote "if there was a significant and material change in circumstance" from that which prevailed in 2014, such as Scotland being taken out of the EU against its will.
"I think an independence referendum is now highly likely, but I also think it's important that we take time to consider all steps, and to have the discussions, not least to assess the response of the European Union to the vote that Scotland expressed yesterday," she said. "I am absolutely determined in my responsibility to give effect to how Scotland voted yesterday."
Sixty-two per cent of Scottish voters backed remaining in the EU, and Sturgeon said that it was "democratically unacceptable" for it to have to be taken out of the EU against its will.
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She called for the Scottish government to be fully involved in all discussions between Britain and the EU and said she will seek direct negotiations with other European states with the aim of keeping Scotland in Europe.
"If (the Scottish) Parliament judges that a second referendum is the best or only way to protect our place in Europe it must have the option to hold one," Sturgeon said.
Scotland could not stage a second referendum without consent from the UK Parliament.
Pro-independence business leaders have also called on the Scottish government to begin talks with the EU to try to keep Scotland in.
"The Scottish government should immediately begin talks with the EU for Scotland to remain a member, even though the rest of the UK may exit, and to clarify that an independent Scotland would be the continuing member state, inheriting the UK's EU membership in the event of a 'Yes' vote in a Scottish independence referendum," said Gordon MacIntyre-Kemp, chief executive of Business for Scotland.