The figure means the authority remains on track to meet its commitment of 30,000 affordable homes by 2016.
The housing statistics, release by the Scottish Government, also found that house-building across all sectors remains higher in the country than the rest of the UK, despite a fall in the completion of new homes.
For the year to the end of June 2013, there were 13,478 new build completions, a fall of 14% compared to the previous year, while private sector starts to the end of June 2013 were 11% lower than 2012. Social sector starts had increased by 2% at the end of September 2013 compared to the previous year.
Commenting on the figures, Housing Minister Margaret Burgess said: "Today's statistics show we are on track to delivering our commitment of 30,000 affordable homes during the lifetime of this Parliament. However they also underline the continued negative impact that challenging global economic conditions and Westminster's cuts to our capital budget have had on house building activity in Scotland.
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"For this Government housing is and will remain a priority. We have boosted our budgets for new affordable homes considerably and in the three year period between April 2012 to March 2015 plan to invest £970 million in affordable housing. This will increase the supply of affordable homes and deliver vital support for construction and house building companies throughout Scotland.
"Housing initiatives such as CRE's '1000 homes for Edinburgh', which, in partnership with the City of Edinburgh Council, is making use of the Scottish Government's Housing Association Grant Recycling Pilot, are crucial in providing mix-tenure homes for Edinburgh residents, while also supporting the construction industry and creating more local jobs.
"We are doing all we can to facilitate the industry's recovery, deliver more affordable homes for people across Scotland and protect and create jobs.
"In particular, our Help to Buy (Scotland) shared equity scheme and our support for MI New Home is helping households get onto or move up the property ladder, whilst our National Housing Trust initiative and House-building Infrastructure Loan Fund are also supporting the construction of much needed new homes."
Castle Rock Edinvar's (CRE) '1000 new homes for Edinburgh initiative' will provide more affordable homes in the capital.
(JP/CD)
