It was also estimated that completing the line from Edinburgh Airport to Haymarket, west of the city centre, would take the cost to £700m.
The official report said building the line as far as St Andrew Square in the city centre would cost £770m.
Councillors will decide the fate of the project at a meeting next week. The original cost of the project was £545m.
That had been the figure for running the line through the city centre and on to Newhaven in the north of the city.
A contractual dispute between the tram company Tie and contractors Bilfinger Berger pushed the project over budget and behind schedule.
Mediation talks are understood to still be under way after the initial meetings between Tie and Bilfinger Berger were held in Glasgow in March.
In May, a report published by Edinburgh City Council said work so far had cost £440m - about 80% of the original budget - with huge sections of the line still to be completed.
Edinburgh councillors ordered a report to be written by officials into the estimated costs of scrapping the tram project.
The report was due out on Thursday, however, the costs were leaked a day early.
A full council meeting will be held on Thursday June 30 to decide the future of the scheme.
The leaked news led Labour councillors in Edinburgh to call for a public inquiry into the tram project.
Andrew Burns, Edinburgh City Council's Labour leader, said: "This is a project which Audit Scotland gave a clean bill of health in June 2007.
"Since then it has totally unravelled.
"I believe it would be wrong to commit further public money to trams.
"We have supported this project since inception, we have attempted to provide positive input while in opposition, yet we feel that the project must be completed within the current funding arrangement."
Marco Biagi, the SNP MSP for Edinburgh Central, said he had serious doubts about the figures for both scrapping the scheme and for completing it.
He said: "I certainly think that the cost of completion to St Andrew Square is an underestimate as indeed all the previous works have been."
Mr Biagi added that the cost of scrapping the project could also be wrong.
He said: "The people who were putting together the figures have an interest in making them appear as big as possible so that the project would go ahead."
A spokeswoman for the City of Edinburgh Council said: "Councillors will next week make a decision on the options for going forward regarding the tram project.
"The costs associated with the various options for phase one of the tram project are still subject to commercial negotiations and legal scrutiny.
"In accordance with the outcomes of the mediation process in March we cannot publicly divulge these figures until both parties have agreed to do so."
A spokesman for Transport Scotland, the Scottish government agency responsible for major public transport projects, said: "The Scottish government opposed the project, but in June 2007 the Scottish Parliament voted in favour of funding up to a maximum of £500m - a figure that ministers will not increase.
"The project is and always has been the responsibility of City of Edinburgh Council and the cost of cancellation or taking the trams project forward is a matter for them."
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