The result is that about $10 billion a year, roughly a quarter of the nation’s university research budget, will continue to be channeled into such things as administrative salaries and building depreciation instead of directly into scientific studies.

Critics say the system lacks accountability, unfairly rewards the biggest schools, and is an ineffective use of taxpayer research dollars in an era of fiscal austerity.

Harvard, for example, gets 69 percent in extra funding, among the highest in the nation and well above the national average of 52 percent.

“Harvard is taking the government to the cleaners,” said Richard Vedder, director of the Washington-based Center for College Affordability and an economics professor at Ohio University, a public college that receives overhead compensation at the rate of 48.5 percent.

“The amount of taxpayer money that goes to support these private schools is immense, and of course, Boston is at the epicenter of this. The federal government should not be in the business of subsidizing building construction or administrative aggrandizement.”

All research institutions get additional money tacked on to federal science and medical grants to help pay for general overhead. But federal rules allow institutions to deposit those payments into their general budgets, with no requirement they be used to directly support scientific endeavors.

The Obama administration sought to change the system last year, saying it was considering a flat rate, at an unspecified level, for all institutions. But after successful lobbying by large universities to protect their bigger share of the pie, the administration abandoned the effort.

Instead, it now suggests institutions should be given a pathway to lock in their existing, higher reimbursement rates for up to four years.

Harvard and other university officials argue that the overhead rates they have negotiated with government agencies reflect real costs to the university, and do not come close to covering the actual amounts that universities spend on building maintenance, staff, and energy costs in pursuit of groundbreaking research.

“Capping rates basically means you’re not going to reflect the actual cost of the research,” said Kevin Casey, an associate vice president who oversees Harvard’s government relations in Washington. “If the government had to create its own facilities, hire the researchers, staff and train students, it would be a more costly venture than to purchase research where it is now.”

Officials from the Office of Management and Budget would not speak on the record about the ongoing rule-making process, or the failure of the overhaul attempt.

“It was shot down big-time,” said a Health and Human Services official who is not authorized to speak to the media. “Universities were too powerful. In a nutshell, the lobbyists killed it.”

Demands for a fairer system have been issued for years, the inequities cited in numerous reports. Vedder and other critics contend the varying overhead reimbursement rates contribute to a widening gap between rich and poor schools. And smaller, less prestigious schools around the country are tired of being shortchanged, particularly when the prime beneficiaries are extremely wealthy schools like Harvard, which has a $30.7 billion endowment.

Bin Guo, a cancer researcher at North Dakota State University who wrote to the government in support of an overhaul, said he supports a flat rate set between 40 and 50 percent. North Dakota State receives a 44.5 percent overhead rate.

“This will eliminate the waste of federal funds at many large institutions that spend the indirect cost on nonresearch-related programs,” Guo said. “If the NIH can save this extra money, they can support more research grants.”

Harvard received $656 million last year in federal research funding, and about $175 million of that was overhead compensation. Harvard maintains that its rate is high because the type of research that is done there requires high-tech facilities and equipment, in addition to being located in a region with high labor and construction costs.

At Boston University, the overhead rate is 63.7 percent, compared with 56 percent at MIT, 53.5 percent at Tufts University, and 55.5 percent at Northeastern.