The Labour and Nationalist groups on the city council finally reached agreement to go ahead with a coalition yesterday, after five days of negotiations.
It was expected to be rubber-stamped by Labour’s Scottish executive (SEC) last night, but instead it decided it wanted to study the proposals in more detail.
A source said one concern was that the proposed coalition would not command a majority on the council.
Following last week’s elections, the SNP is the largest group with 19 seats and Labour has 12, so together they fall one short of an overall majority on the 63-strong council.
However the Greens have said they would offer support where there was policy convergence.
And a source said: “An SNP-Labour coalition with the numbers we’re talking about would only risk defeat if the Tories, Greens and Liberal Democrats all came together against them, which is not very likely.”
The Tories – just one behind the SNP with 18 seats – have argued for a “pan-unionist” coalition involving themselves, Labour and the six-strong Liberal Democrats, but it is understood the Labour group has privately ruled that out.
Labour and the SNP were in a joint administration for the past five years, with Labour as the lead partner, but the new Labour group is said to have been divided on whether to go back into coalition with the SNP, with some councillors vehemently opposed to throwing in their lot with the Nationalists at a time of heightened political tensions.
SNP sources have claimed the group came under pressure from Ian Murray, who is fighting to get re-elected for Labour in Edinburgh South, and his Holyrood counterpart Daniel Johnson to stay out of coalition with the Nationalists.
Mr Murray denied he had been trying to influence the coalition talks and angrily rejected the suggestion he favoured a deal with the Tories. “That is completely fabricated,” he said. “I have had nothing to do with this process. I have not had a conversation with Cammy since Friday when I wished him well.”
Mr Johnson also said the suggestion he advocated a deal with the Tories was “straight up not true”.
But he warned a coalition with anyone could prove difficult. He said: “The Scottish Labour position on local deals is clear and cast iron. Coalitions are only possible if they protect local services from cuts. Unless there is a guarantee that budgets are protected it will be very difficult for Labour to enter into a coalition with any party in Edinburgh.
“We also have a fundamental difference of opinion with the SNP regarding the issue of independence. Any deal is of course a matter for the Labour group on the city council subject to SEC approval, but these are challenging tests to meet and I remain extremely cautious about any possible deals with any parties.”
Labour’s executive meets again tonight, but a spokesman said there was no guarantee the deal would be approved then.