It says some of the doubted savings are caused by government departments struggling to account for their efficiencies, while others are caused by suspicions of "inaccurate measurement".
"A focus by government on the efficiency of its departments is extremely important," PAC chair Edward Leigh MP said in a statement.
"But efficiency gains must be real and demonstrable. They must be deliverable year after year and not be one-offs. The cost of achieving them must be taken into account. And they are not genuine if, as we have found in a number of cases, they are achieved at the expense of the quality of the service provided."
Report paints 'grim picture'
The Conservatives' shadow chief secretary to the Treasury, Philip Hammond, said the report "paints a grim picture" for the government.
"Not only are nearly three-quarters of the government's claimed savings potentially bogus, but vulnerable families may be suffering because of deteriorating services," he said.
"After a shameful week of spin from Labour, this is yet more evidence of Gordon Brown dressing up the government's achievements to make himself look better."
A Treasury spokesman said a response to the report was being prepared.