Sturgeon said in the Scottish Parliament's first debate last week that she's open to discussions on the timing of the vote if the United Kingdom presents "a clear alternative and the rationale for it", though she insisted that she has a mandate to call a referendum because Brexit means the status quo is no longer an option. She added: "The people of Scotland are sovereign, and they will be given a choice on their own future".
Scotland's First Minister Nicola Sturgeon attends a debate on a second referendum on independence at Scotland's Parliament in Holyrood, Edinburgh, Britain, March 28, 2017.
The United Kingdom as a whole voted previous year to leave the European Union, but Scotland, one of the UK's four constituent parts, voted to stay.
Ms Sturgeon's motion passed by 69 votes to 59.
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Sturgeon said after the vote that she would "seek sensible and constructive discussion" with the British government later this week.
Sturgeon is pressing for a referendum in the second half of 2018 or the first half of 2019, before Britain leaves the European Union, but May has told her "now is not the time".
Her comments came as members of the Scottish Parliament prepared for a second day of debate on SNP plans for a second referendum, after last week's session was postponed as a result of the attack in London.
The mandate for a referendum is beyond question, and it would be democratically indefensible - and utterly unsustainable - to attempt to stand in the way of it.
The Scottish Tories, Scottish Labour and the Liberal Democrats voted against giving the Scottish Government that consent.
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May previously said "now is not the time" to discuss a referendum.
But Britain government has already said it will block a referendum until after the Brexit process has been completed.
Neither leader has expressed a willingness to compromise and the rift is unlikely to end before Article 50 is triggered.
The Scottish government can not, however, hold a binding referendum on independence without the approval of the government at Westminster.
May will send a letter to EU President Donald Tusk with Britain's formal departure notification on Wednesday, opening up a two-year negotiating window before Britain actually leaves the bloc in 2019.
"I made clear the Scottish Government wants to play its part as it is in all our interests that she secures a good deal".
"If I ruled out a referendum, I would be deciding - completely unilaterally - that Scotland will follow the United Kingdom to a hard Brexit come-what-may, no matter how damaging to our society it turns out to be. It is that now is not the time to be talking about a second independence referendum", she said Monday.
May also said Monday that "now is the time when we should be pulling together, not hanging apart".
She will say: "And that is important to remember".
At one stage, Scottish Conservative leader Ruth Davidson told Sturgeon to "sit down" during a heated exchange with the Scottish First Minister.