Opinion polls have in the past few days shown unexpectedly strong support for leaving the European Union in a June 23 referendum, a step that could rock the EU, test the unity of the United Kingdom and unleash turmoil on global financial markets.

"Clearly the referendum is on a knife edge across the UK," Sturgeon, the pro-EU leader of Scotland's devolved government, told Reuters in an interview in the Scottish Parliament.

Sturgeon said that if England pulled the United Kingdom out of the EU and Scotland voted to stay, there would probably be sharp rise in support for calling a vote on Scottish independence. She declined to give any timescale.

Scots rejected independence by 55-45 percent in a referendum in September 2014, though the vote energised Scottish politics and support for Sturgeon's Scottish National Party (SNP) has surged since then.

Because of the potential political uncertainty that a so-called Brexit would cause, it is unclear how much support there would be for secession if Scots were to vote on the issue again.

Sturgeon, 45, has been campaigning for Britain to remain in the EU, which she says is good for jobs, businesses and workers' rights.

"It would be a very serious mistake for the UK to vote to leave the European Union, and I think it would be democratically indefensible for Scotland, if we had voted to stay in, to face the prospect of being taken out," Sturgeon said.

"If we were to find ourselves in that position then I think people -- you know even people who don't support Scotland becoming independent -- in all fairness could understand the sense of disquiet that there would be in Scotland over that."

Many Scots voted to remain in the United Kingdom in the 2014 independence referendum because they wanted to remain in the EU, said Sturgeon.

Sturgeon was this month rated by U.S. magazine Forbes as the world's 50th most powerful woman and Britain's second most powerful after Queen Elizabeth. Her approval ratings amongst Scots are near 60 percent, according to pollster YouGov. 

UNITED KINGDOM?

Since Sturgeon took over the SNP leadership following the independence referendum, party membership has risen fivefold. In an election in May 2015, the pro-independence party won 56 of the 59 seats allocated to Scotland in Britain's Westminster parliament.

As head of the devolved Scottish government, Sturgeon decides health and education spending in Scotland and has the power to set some tax rates and bands.

She expressed concern about the future of British politics in the event of a Brexit, saying right-wing politicians could unseat Conservative Prime Minister David Cameron, who is also campaigning for Britain to remain in the EU.

"I worry about the direction of the UK and UK politics and governance in the event of a Brexit," Sturgeon said. "If there is a 'Leave' vote in England and across the UK as a whole then we see the reins of power being seized by politicians who are on the right of the Conservative party."

"It is absolutely vital to get out there in big numbers and (vote) remain."