Ruth Davidson’s party won 25.3 per cent of first preferences at the ballot on May 4, an increase of 271,474 votes from the last council elections in 2012.
Labour saw their share drop 11 points to 20.2 per cent.
The SNP claimed 32.3 per cent of first preferences, with an overall increase of 80,221 votes.
The Nationalists insisted the figures from the Election Management Board proved it had won the elections.
The party emerged from Thursday’s vote with 431 councillors, an increase of six from 2012, while the Tories boosted their town hall ranks by 161, with a total of 276.
“The SNP has won the local elections emphatically, with more seats than any other party, an increased and higher share of the vote than any other party and as the largest party in more councils than any other party,” said party campaign manager and MSP Derek Mackay.
But James Kelly, Labour’s campaign manager in Scotland, said the result proved the First Minister “could longer claim to speak for all of Scotland”, having secured less than a third of votes.
“It’s official - the Sturgeon surge has turned into a Sturgeon slump with the threat of a divisive second independence referendum hanging over Scotland,” he said.
“How can Nicola Sturgeon claim to speak for all of Scotland having secured less than a third of the vote?
“In 2015 the SNP secured half of the Scottish vote, and these official figures show that has now plummeted by 18 points.
“It is clear that more and more people are getting sick and tired of the SNP’s obsession with dividing us again.
Both the Greens and Lib Dems saw small increases to their number of first preference votes, 1.8 and 0.2 per cent respectively.