Ms Sturgeon had been expected to win the backing of a majority of MSPs for her plan to ask the United Kingdom government for a section 30 order, which would be needed to hold a legally-binding referendum on independence.
"For the UK Government to stand in the way of Scotland even having a choice would be, in my view, wrong, unfair and utterly unsustainable", Sturgeon, Scotland's first minister, said on Tuesday. In the first referendum in September 2014, more than 55 percent of Scottish people voted to remain a part of the United Kingdom.
British Prime Minister Theresa May on Friday accused the SNP of "divisive and obsessive nationalism" and defended the "precious, precious union" of England, Scotland, Northern Ireland and Wales.
Sturgeon has said that she wants a new vote on independence to take place between the autumn 2018 and spring 2019, when the terms of Britain's departure from the European Union will have become clearer.
The debate was suspended on Wednesday afternoon following the terror attack in London that has left four people dead.
If the semi-autonomous Scottish Parliament does vote in favor of a referendum - as is widely expected - it will mean that advocates for Scottish independence will be able to say they have a parliamentary mandate for a referendum.
Police vehicles were seen outside the parliament building, with a spokesman for Police Scotland saying the force was "liaising with colleagues in London and will ensure appropriate safety and security plans are in place based upon what we know".
But that position is likely to change, though the timing of a new referendum remains subject to debate.
Sturgeon's demand for a second referendum is far from universally popular in the Scottish Parliament.
An appeal from the Scottish Conservative Party, allies of the UK Government and the main unionist opposition in Edinburgh, to have the debate suspended shortly after the attack was initially rejected.
"They are now terrified of the verdict of the Scottish people", she told supporters in the city of Aberdeen.
Kezia Dugdale, leader of the Scottish Labour Party which will also oppose the motion, was similarly scathing.
So will the motion pass?
The SNP runs a minority government with 63 of the 129 seats in parliament.