Tommy McLean, chairman of Corstorphine Community Centre, appealed to the council’s finance and resources committee for help plugging a £750,000 funding gap to redevelop the facility – which was destroyed by fire in 2013.
Mr McLean told councillors that organisers had “exhausted all other sources” of funding available to them.
He added: “There have been substantial funding efforts made by the local community. We are a really important facility for the area and they are really missing it at the moment.
“The expected cost of the building is about £2m plus VAT. There’s a great local community spirit, we just need some additional help.”
But a row erupted after Mr McLean revealed that leader of the council, Cllr Adam McVey, depute leader Cllr Cammy Day and lord provost Frank Ross had given him assurances that a funding bid would be supported in a private meeting earlier this year.
Mr McLean said: “We were given strong hope that we would get it.
“We had discussions with the leader of the council, deputy leader and lord provost. At that meeting we were certainly given strong encouragement that the council was very supportive.”
A council source suggested that SNP councillors were keen to commit to funding the project in order to “win electoral support” in the west of Edinburgh, while Labour councillors were “nervous” about pledging support for the development in the current difficult financial climate.
The council has not issued capital funding towards other community centres this year.
Conservative finance spokesperson, Cllr Graham Hutchison, said both partners of the coalition were “unsurprisingly not singing form the same hymn sheet”.
He added: “I think this council has done an enormous disservice to the people in Corstorphine by producing a report less than 24 hours before this meeting takes places.
“Senior members of this council have sat down and given some comfort to the board about £750,000 of funding when it’s clear we have never had a means of delivering £750,000.”
Green finance spokesperson, Cllr Gavin Corbett, also raised concerns about the private meeting.
He said: “If that’s the case that senior councillors have given them expectations that weren’t verified here, that’s unfair and shouldn’t happen again.”
But council leader, Cllr McVey has hit back at the claims.
He said: “When we set the council’s budget in February, I made the SNP’s support for the Corstorphine Community Centre clear.
“The community group should be commended for their efforts and commitment to delivering this project for the people of Corstorphine and wider and we’re determined to find a way of enabling work to build the new community centre to start.
“When I met the community group earlier this year I was happy to reiterate that support. It’s in all our interests to support community based projects like this and we’ll continue to work with other political groups, Council officers and the community to ensure that happens.”
Councillors agreed that officers will “use their best endeavours” to help the community centre board “identify all possible funding solutions” – which could include “consideration in the capital spending review” in December.
Finance and resources convener, Cllr Alasdair Rankin, said: “We have suggested a clear way forward – without making commitments which we’re either not in a position to make or other funders involved aren’t able to make.
It may not be in the time-scale that some members I happen to know might have wanted but nevertheless, I think it is a clear way forward.”