The Scottish parliament is expected to vote on Wednesday to endorse Sturgeon's call for a second vote, less than three years after Scots rejected independence in a 2014 referendum.
Sturgeon's Scottish National Party (SNP), which runs the semi-autonomous government in Edinburgh, says Britain's vote to leave the EU means Scots should be able to reconsider.
She called last week for a vote between autumn 2018 and spring 2019 -- before Brexit, which now looks set to take place in March 2019.
May has said that "now is not the time" for a new vote, and can block Sturgeon's request even if the Scottish parliament approves it this week.
But the SNP leader has said such a move would be "democratically indefensible", although she has signalled she is willing to negotiate on a date.
"This crucial decision over our future should not be made unilaterally by me, or by the prime minister," Sturgeon said.
"It should be made by the people of Scotland, and I call on parliament to give the people that choice."
She said her Brexit compromise for Scotland to be allowed to remain in the European single market even as the rest of Britain leaves had been met with "a brick wall of intransigence" in London.
The SNP does not have an outright majority in the Scottish parliament, but it has already secured the support of the Green party for another independence bid.
Patrick Harvie, leader of the Greens, said: "I think Theresa May will be taking a huge risk... if she refuses to acknowledge that we have a right in Scotland to have a say about our future."
'No public or political consent'
Scotland voted against independence by 55 percent in September 2014, but the campaign left the unionist camp politically divided while nationalists flocked to the SNP in droves.
The SNP won all but three Scottish seats in the British parliament in 2015 and Sturgeon was re-elected to the Scottish assembly in May 2016 on a pledge to hold another independence vote if Scotland was "dragged out" of the EU against its will.
The SNP gained twice as many votes as the other parties, and Scotland was outvoted by England and Wales in the Brexit referendum in June 2016, sparking a fresh constitutional crisis.
But Sturgeon has yet to convince a sceptical electorate, with a series of recent polls showing support for independence has barely moved since 2014 -- including a Panelbase poll concluded on Friday which found it stood at 44 percent.
"We believe a referendum cannot happen while the Brexit process is being played out," said Scottish Conservative leader Ruth Davidson, May's most senior representative in Edinburgh.
"We believe a referendum should not happen when there is no public or political consent for it to happen."
John Curtice, professor of politics at the University of Strathclyde, suggested May's intransigence and the current lack of public support for another referendum may actually work in Sturgeon's favour.
"The 'Yes' side still has considerable ground to make. More time to argue her case might, in truth, be just what Nicola Sturgeon wants," he said.
Warning about job losses
One of the arguments that helped sway Scottish voters in 2014 was the economic uncertainty that would come with independence.
Critics say the situation is now worse, after a fall in oil prices has hit Scotland's energy industry and blown a hole in its public finances.
However, Sturgeon has warned that leaving Europe's single market will causes tens of thousands of job losses in Scotland.
"If the oil price remains low and if they lose the money which is transferred from the rest of the United Kingdom to Scotland, then they would have to make that up in their own budget," former Bank of England governor Mervyn King told the BBC.
"But that's a consequence of deciding to be financially independent, you end up paying for yourself."
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