Nicola Sturgeon said she does not want Tories “obsessed with austerity” in charge of local services.
She urged people to vote SNP for “strong champions in local councils”.
After the 2012 council elections the SNP formed coalitions with the Tories in Dumfries and Galloway and in East Ayrshire.
Asked on BBC Scotland whether the SNP would be willing to go into coalition with Tories in some councils, she replied: “No. The SNP national executive committee took the decision on Saturday that we wouldn’t have coalitions with the Tories after these elections and the reason for that is simple.
“We are looking at a Tory party that is moving further and further to the right.
“The Tory party has been taken over by its right wing. I don’t want those right wing Tories taking over council services.”
She added: “We’re facing a Tory party that is increasingly in thrall to its own right wing and I don’t want to see a Tory party obsessed with austerity, with cuts, in control of local services.
“I’m being frank with the people of Scotland, I don’t think it’s in the interests of local services for the Conservatives to run them so I’m arguing in this campaign for votes for the SNP to put the SNP in the strongest possible position coming out of these elections to protect local services and to protect Scotland from the impact and the implications of Conservatives running these services.”
Ms Sturgeon urged people to look carefully at local issues when deciding who to vote for on May 4.
She said: “This is about your local services, it’s about who you think is best placed to protect those local services and one of the big risks in this election which perhaps wasn’t so obvious last time around is the risk of local services falling into the hands of the Tories.
“If you don’t want that then vote SNP for strong champions in local councils protecting your services.”