City leader Jenny Dawe has faced criticism for failing to agree to set up a cross-party campaign for a better funding deal for Edinburgh.
Labour councillor Paul Godzik suggested the measure after finance secretary John Swinney announced last week that capital funding for councils will be slashed by £200 million.
Cllr Godzik said the campaign could help Edinburgh get a better deal when final figures for councils are announced in December – but did not win support from Cllr Dawe.
“At the moment around £100m a year is taken from the Capital in business rates and distributed across the country,” said Cllr Godzik.
“Edinburgh is also said to have three-quarters of Scotland’s affordable housing need, but receives only 25 per cent of the funding.
“I recognise that there are real budget pressures, yet that makes it even more critical that we should be doing everything possible for Edinburgh.”
Cllr Ricky Henderson, finance spokesman for the Labour group, said: “Edinburgh Labour are determined to fight for a fair deal.”