Ms Sturgeon said she agreed with Ms May that it would be wrong to hold a referendum immediately, but said one should take place after the terms of Brexit were agreed and a deal on future trade with the European Union was struck, something Ms May believes will happen before March 2019.
Scottish Liberal Democrat leader Willie Rennie said: "There will be many voters who voted to remain in the European Union who will be feeling betrayed by the SNP who are simply using Brexit for their own ends".
"So, I hope the prime minister changes her mind and acknowledges the people of Scotland are entitled to a choice at a time and in a way that is right for Scotland".
Citing a Scottish parliamentary vote on Tuesday to back her request for those powers, Sturgeon said she had a clear mandate to pursue a referendum based on long Scottish traditions of "popular sovereignty".
Sturgeon will send a letter today to Tory Prime Minister Theresa May requesting a second referendum.
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In a letter to Prime Minister Theresa May, Sturgeon asked for Section 30 order to allow the Edinburgh government to legislate for a referendum.
The Scots want the vote to take place between autumn 2018 and spring 2019.
Sturgeon announced her intention to hold a second referendum earlier this month.
Opening the debate, Sturgeon demanded Westminster should respect the wishes of the Scottish Parliament.
The Scottish Parliament has already agreed to seek powers for a poll among the people of Scotland, but it can only go ahead with Westminster's approval.
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"I hope that will be by constructive discussion between our governments".
Sturgeon said there appeared to be "no rational reason" to deny a vote.
Ms May's Downing Street office confirmed that the letter had been received.
"However if it chooses not to do so, I will return to the Parliament following the Easter recess to set out the steps the Scottish Government will take to progress the will of Parliament".
In the letter, Ms Sturgeon said that although the Brexit negotiations are yet to get underway, it seems inevitable the outcome will leave the United Kingdom outside the European single market.
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But Jackson Carlaw MSP, the deputy leader of the Scottish Conservatives, said Sturgeon's proposal was both "unwanted and unworkable" until voters north of the border have a chance to see Brexit play out".