With average house prices nearing ten times the average salary, Ewan Aitken, the leader the city council, said 6,000 people are bidding for only 60 affordable rented homes in the city every week. Last week, 720 people bid for one council house in Stenhouse.
Housing experts said the chronic shortage in the capital could slow the whole economy down if it is not addressed soon. They have suggested building would have to begin on green-belt land in the long term.
Ivan Turok, a professor of urban economic development at Glasgow University, said Edinburgh had an advantage in being able to persuade private investors to build a proportion of affordable housing, because house prices remain high.
He said derelict land can be reclaimed, although ultimately there must be "strategic use" of green-belt land. "I think it is almost certain that Edinburgh will have to relax parts of the green belt in the end to allow more development," he added.
Prof Turok warned that the problem of affordable housing was most serious in the capital, but was having an impact on the whole of Scotland.
"The affordable housing problem in London is in danger of holding back the UK economy. If you look at Scotland as a microcosm of the UK, we have a similar problem on a smaller scale," he said.
Unlike the rest of Scotland, Edinburgh has a rising population as more people come to live and work in the capital. More housing is also required as a growing number of people choose to live alone.
Mr Aitken called for a city-wide trust that will bring together public and private investors to build 12,000 homes in the next decade - although he was at a loss to be able to specify where the new houses will be built.
However, Mr Aitken said the capital is still getting too little public funding. Edinburgh receives £36 million for building affordable housing, compared with £90 million for Glasgow.
Speaking at The Future for Housing conference in Glasgow, Mr Aitken called for a private public trust fund to be set up to build 12,000 houses over ten years.
"At a minimum, I want to see a partnership between public and private sector investors that can raise the £2 billion I believe is needed over the next ten years to meet the demand for affordable rented homes," he said.
"[The] solution will only come when we have the investment and land to build at least 12,000 new homes over the next ten years."
Mr Aitken said Edinburgh has already secured enough land for 4,500 houses at Craigmillar, Granton and the south-east wedge.
He also hoped to gain more land from private investors by asking them to put 25 per cent of any development towards affordable housing.
"I am not going to say at the moment that we are going to build on green-belt land at the moment, because that is too big a step for us, but I would understand why someone else would say it," he said.
Archie Stoddart, a director of Shelter Scotland, said the lack of affordable housing is forcing people on to the streets or into temporary accommodation.
He said Scotland needs 30,000 new houses over the next three years, at a cost of £750 million.
"We must raise housing problems from a grassroots level to the top of the political sphere if we are to truly help people in housing crisis in Scotland," he said.
The Executive said it is working on providing more affordable housing by building 8,000 homes over the next year, at a cost of £584 million.


