The Scottish Parliament has backed a second independence referendum, as Westminster reiterated its refusal to negotiate on allowing one.
Sturgeon wants to hold the referendum between autumn next year and spring 2019 but the UK Government has said it will block one until Britain has left the EU.
Sturgeon has said there is an “unquestionable democratic mandate” for a referendum, after Scotland voted Remain and May’s Government appears set on withdrawing from the Single Market.
For a referendum to go ahead in Scotland, it will have to be approved by Westminster.
Secretary of State for Scotland David Mundell said it “simply wouldn’t be fair to hold a referendum during the Brexit process”.
He added: “We are not entering into negotiations on whether there should be another independence referendum during the Brexit process.
“We don’t have a crystal ball as to how long that process will take. We don’t recognise, for example, 18 months as being a key point in the journey.
“It will be a journey that will involve the negotiations with the EU, it may be a journey that involves transitional measures, it may be a journey that involves significant implementation time.”
A UK government spokeswoman said: “We have been joined together as one country for more than 300 years.
“We’ve worked together, we’ve prospered together, we’ve fought wars together, and we have a bright future.
“At this crucial time we should be working together, not pulling apart.”
Reacting to the vote, Sturgeon said the Scottish Government would now “seek sensible and constructive dialogue” with Westminster and would wait until after Article 50 is triggered - beginning the two-year Brexit negotiations - on Wednesday.
She called on the British Government to “respect the will” of the Scottish Parliament.
This is simply about giving people in Scotland a choice. We agree now is not the right time for that choice but that choice should be available to people when the terms of Brexit are clear Nicola Sturgeon
“This is simply about giving people in Scotland a choice,” she told reporters. “We agree now is not the right time for that choice but that choice should be available to people when the terms of Brexit are clear.”
The vote in Holyrood was due to be held last Wednesday but was postponed in the wake of the terror attack in London.
Sturgeon said she would set out in April how she will respond if the UK government has still not backed down.
May and Sturgeon met in Glasgow on Monday. There followed an argument over what was said, with Sturgeon suggesting she had secured a concession over Brexit negotiations ending within 18 to 24 months and Downing Street denying it.
She has argued that holding a second independence referendum at the same time would be a distraction.
But Sturgeon told MSPs in Holyrood that the changes that came with Brexit “should not be imposed” on Scotland.
“The people of Scotland should have the right to choose between Brexit - possibly a very hard Brexit - or becoming an independent country, able to chart our own course and create a true partnership of equals across these islands,” she said.
Speaking during the debate at Holyrood, Scottish Conservative leader Ruth Davidson said: “Last week, in what was a disgraceful episode, we were shouted at from the SNP benches and told that wee were frightened to debate independence.
“We’re not but we are sick of it. And most people in Scotland have had enough too because this parliament needs to and must focus on the priorities of the people of this country and it is not the time to be sidetracked by yet more unnecessary division.”
Scottish Labour leader Kezia Dugdale also opposed a second vote.
“Brexit isn’t the motivation for another referendum, it’s just the latest excuse,” she said.
“We voted decisively to remain in the UK [in 2014]. That’s the will of the people and it should be respected.
“My message to the First Minister remains unchanged: we are divided enough – do not divide us again.”
Scots rejected independence at the last referendum in September 2014, with 55% voting No.
A YouGov poll conducted in March found 43% were backing Yes and 57% were backing No.
About 62% of Scottish voters backed the UK remaining part of the EU in June’s Brexit referendum.
The SNP manifesto for last year’s Holyrood elections made clear another ballot on independence should take place if there were a “material change in circumstances’’ - such as Scotland being removed from the EU against its wishes - from the previous vote in 2014.
The SNP lost its majority at the 2016 Scottish Parliament elections but Tuesday’s vote passed with support from the Scottish Greens.