The First Minister was asked three times by the press if she would forbid SNP groups from forming alliances with the Tories after the local election, and three times refused to say.
The SNP are currently in coalition with Tories on East Ayrshire Council, and a predicted surge for both parties on May 4 could make more combinations possible.
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The two parties have also previously run Dumfries & Galloway council together.
The First Minister’s refusal to rule out further deals came as she launched her party’s local election campaign at a community arts centre in Wester Hailes in Edinburgh.
She went on: “There is a danger, either through people voting Tory or Labour looking at coalitions with the Tories to keep themselves in power in council chambers, that we do in this election see local services slipping into Tory hands, and I think that would be disastrous.
“So my message is very clear and straight: if you want to protect local services, vote SNP.”
But when asked if she would prevent SNP council groups, including in East Ayrshire, forming coalitions of their own with the Conservatives, she skirted around the question.
She said: “I want to see SNP councils. I am going to campaign for the remainder of this campaign to get as many votes for the SNP and as many SNP councils as possible.”
Asked again if she would forbid SNP-Tory coalitions, she said: “I don’t want to see the Tories in council chambers. I don’t want to see the Tories with their hands on local services.
“That’s why my message is crystal clear: vote SNP. We have an election in two weeks’ time, so the way to keep the Tories out of the control of councils is to vote SNP.”
Pressed again on coalitions, she said: “I think anybody who looks at the relationships between the SNP and the Tories right now would think that was hugely unlikely. My main message is vote SNP to make sure you have SNP councillors running councils.”
She said: “There we have it: Labour is unelectable and the Liberal Democrats propped the Tories up for five years and will not rule out doing it again."
Because council elections use the proportional single transferable vote system, coalitions and minority administrations are the norm.
The SNP is currently part of a coalition is six of Scotland’s 32 local authorities.
In the 2012 local election, the SNP was only just ahead of Labour in vote share and councillor numbers, but Labour was able to form alliances in far more councils to gain power.
With the polls showing Labour likely to come third behind the Tories, Ms Sturgeon presented the election as a straight choice between the SNP and Tories, omitting all mention of Labour from her broadcast interviews and from a party political message she recorded on site.
The Scottish Conservatives said: “It’s hard to see why Scottish Conservative councillors would want a coalition with a party that wants to break up the UK, but we’ve made clear this is a decision for local councillors, and not from on high.”
The SNP council manifesto pledges councillors will deliver a raft of SNP government policies.
Unlike the Unionist party manifestos, it does not mention independence or a new referendum.
Labour local election director Alex Rowley said: “Nicola Sturgeon has a brass neck claiming the SNP will stand up to Tory cuts. Since 2011 the SNP has cut £1.5bn from local services.
“Voters have an opportunity to send Nicola Sturgeon and the SNP a message that Scotland doesn’t want another divisive referendum.”
Green Yvonne McLellan added: “Voters will see through attempts by any party to turn the council elections into a vote on the constitution.”