The federal agency that insures pensions for 43 million Americans saw its deficit swell to $34 billion in the past year, the largest in its 38-year history.

In its annual report released Friday, the Pension Benefit Guaranty Corp. blamed the growing shortfall on its inability to charge private employers adequate premiums for insuring pensions.

Citing the increasing deficit, PBGC Director Joshua Gotbaum called on Congress to give the agency power to set its own premiums. “We continue to hope that PBGC can have the tools to set its own financial house in order, the way other government and private insurers do,” he said in a statement.

The Obama administration has called on Congress to give PBGC’s board the power to set premiums. But those efforts have been unsuccessful, in large part because some members of Congress say that a new premium structure could significantly raise costs for companies whose retirement funds already are at risk of running out of money. Although Congress has raised PBGC premiums repeatedly in the past, they have not gone up in recent years.

PBGC is funded by a combination of insurance premiums from private pension plans, investment returns on its $85 billion in assets and recoveries from bankrupt companies. It receives no taxpayer money, and its leaders say it has has sufficient reserves to cover its obligations.

Overall, the agency saw its long-term liabilities increase $12 billion to $119 billion, while its assets grew by $4 billion over the past year.

If the shortfalls continue, Gotbaum warned, “PBGC may face for the first time the need for taxpayer funds. That is a situation no one wants.”

The agency has proposed setting premiums that reflect the perceived riskiness of the pension plans it insures, with financially shaky firms paying more to have their pension promises guaranteed by the agency.

But business lobbyists have branded the proposal a non-starter. They say any increases would work against the agency’s larger goal of enhancing the troubling retirement security landscape confronting many Americans by making it more expensive for the dwindling number of firms that have pension plans to insure them.

Currently, fewer than one in six private-sector workers are covered by defined-benefit pensions, a percentage that has been shrinking for three decades. More than half of private-sector workers have no retirement coverage through their employers.

Meanwhile, 53 percent of Americans are in danger of being unable to maintain their standard of living in retirement, according to the Center for Retirement Research at Boston College.

The agency’s deficit also has been fanned by low interest rates, which under accounting rules makes many troubled pension funds look even weaker.

In addition to its growing deficit, the PBGC said that at the end of 2010 it faced $332 billion in potential liabilities from fiscally unsound plans that could end up in its hands in the future.

In the fiscal year ended in September, the agency paid nearly $5.5 billion in benefits to 887,000 retirees whose plans have failed, and 614,0000 people are expected to collect benefits from the agency once they retire. In that year, the agency also assumed responsibility for the pensions of 47,000 people in newly failed plans.

The agency also is charged with discouraging financially trouble firms from jettisoning their pension obligations. Last year, the agency helped protect the pensions of 130,000 employees of American Airlines, which is in bankruptcy, according to the report.

It also helped preserve the pensions of 37,000 people whose companies have emerged from bankruptcy, including Houghton Mifflin Harcourt Publishing, the food retailer A&P, and the publishing company Lee Enterprises.