She said "another clear win" for the SNP at the General Election next month will "bring it even closer still".
The SNP leader is the headline speaker at the event in George Square, her first speech at an independence rally since the 2014 independence referendum campaign.
Ahead of the event, she said: "A vote for the SNP is a vote to escape Brexit, and to put Scotland's future in Scotland's hands - not Boris Johnson's.
"This election really is the most important one Scotland has faced in modern times.
"So much is on the line - people are completely fed up with the mess at Westminster.
"But George Square will be packed today as people from all backgrounds join together to demand a better future for Scotland.
"An independent Scotland is closer than it has ever been. It really is within touching distance.
"What is needed now is another clear win for the SNP to bring it even closer still - so vote SNP on December 12th to secure Scotland's right to decide."
The First Minister used her speech to the SNP conference in Aberdeen to insist a second independence referendum "must" take place in 2020.
She will formally request the power for Holyrood to stage a referendum from Prime Minister Boris Johnson before the end of this year.
A section 30 order - which the UK Government has so far refused to consider - would mean a legally binding ballot could be held.
Also speaking at the rally, organised by Scotland's only pro-independence daily newspaper The National, are fellow SNP members Mhairi Black MP, Justice Secretary Humza Yousaf and Scottish Green co-leader Patrick Harvie.
Mr Harvie will appeal for an "inclusive" campaign for a second independence referendum to protect people from the "hard-right Brexit project".
Speaking ahead of the rally, he said: "The cause of Scottish independence must be broad and inclusive. Our diversity is our strength.
"Those people who are still to decide need to be offered a positive, hopeful vision about how we can live in a fair, equal, sustainable country, and why independence will help."
But Scottish Labour leader Richard Leonard insisted: "The last thing Scotland needs is another divisive independence referendum."
Mr Leonard, who will be campaigning in Coatbridge on Saturday, said: "While Nicola Sturgeon is speaking to her own supporters, Labour is out on the streets of Scotland speaking to voters.
"We are putting forward our positive case for a Labour government that will scrap Universal Credit, introduce a £10-per-hour real living wage and deliver £70 billion of extra investment in Scotland's public services."
Scottish Secretary Alister Jack meanwhile said the SNP would "absolutely" not have a mandate for a second independence referendum if wins the most seats north of the border on December 12.
The Tory MP told The Herald newspaper: "I'm absolutely saying they would not have a mandate.
"To me it's very simple. We had a once-in-a-generation, her words, once-in-a-lifetime, she and the First Minister at the time Alex Salmond used those expressions, referendum in 2014, we had that, the people of Scotland decided to stay in the UK and they should respect that referendum and they should respect the referendum in 2016, which was a UK one."