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The two parties were in coalition together in the Capital up until last week’s elections and Councillor McVey said they had worked well together.
The SNP was returned as the biggest party on the council with 19 seats, Labour has 13, the Lib Dems 12, Greens 10 and Tories nine.
The signs over the past few days were that Mr Sarwar’s stance was making an SNP-Green coalition the most likely outcome of the talks taking place across parties about a new administration for Edinburgh.
But now Councillor McVey has made clear he still hopes to reach some kind of agreement with Labour. He said: “The most logical option from the result remains a two-party coalition majority coalition. We are the only two parties that make a two-party majority, so discussions will continue to see if there's a version of collaboration, of working together that can mean those two manifestos, which were very similar, can be progressed – because ultimately that's what the people of Edinburgh voted for.
"We're continuing to have discussions with a number of parties, but a collaboration of some description between the two parties that can deliver an element of certainty is still the most logical outcome.”
It is unclear what kind of arrangement the SNP and Labour groups could come up with which Mr Sarwar and the Scottish Labour party would be willing to accept. Sources have suggested attempts by Labour group leader Cammy Day to gain some leeway for doing a deal in Edinburgh have been firmly rejected by Labour headquarters.
Even an informal deal which did not involve a written agreement could fall foul of Labour’s national stance, especially if it included Labour councillors taking posts in the new administration.
And Councillor Day may also have trouble persuading his Labour group a deal with the SNP is the right move. Ross McKenzie, the newy-elected Labour councillor for Sighthill/Gorgie tweeted yesterday: “Being a junior coalition partner to the SNP requires participation in a cover-up of the extent to which that party is underfunding local government and outsourcing the services it provides.”
Although the SNP and the Greens are in partnership in the Scottish Government, making a deal between the two parties at local level an obvious option, it is understood both Councillor McVey and the Edinburgh Greens have felt uneasy about forming a coalition which would fall short of a majority of seats on the council, leaving the administration vulnerable to defeat by a combined opposition. A deal between the SNP and Labour would remove that risk.
Councillor McVey said: “We think the most straightforward way forward is the two parties working together who have been delivered a majority of seats by the people, on manifestos which are very similar. It makes sense to work together in some form to try to deliver those [manifestos] with an element of certainty, without a minority situation that means strange things can happen on any given day which can undermine the progress you’re trying to make.”