Geithner made the new estimate in a letter Friday to congressional leaders that was obtained by The Associated Press.
A year ago, officials were estimating the bailout could cost as much as $500 billion.
The new estimate said the biggest losses will occur from the government's support of mortgage companies Fannie Mae and Freddie Mac. That loss was put at $85 billion followed by a loss of $49 billion from providing help to homeowners facing the threat of losing their homes through foreclosures.
Geithner's letter estimated that the government would lose $48 billion through the support provided to insurance giant American International Group and another $28 billion would be lost through the billions of dollars in assistance provided to General Motors, Chrysler and their auto financing arms.
The biggest offset to those losses will be earnings of $115 billion that the administration expects the Federal Reserve to realize from the extraordinary assistance it has given to provide liquidity to the financial system.
The new estimates, which President Barack Obama is expected to cite in his weekly radio address on Saturday, are part of the administration's intensified lobbying campaign to get Congress to pass sweeping financial overhaul legislation.
Democrats have set an initial showdown vote for next Monday on legislation pending in the Senate. The House has already passed its version of what would be the most sweeping overhaul of the financial system since the 1930s.
"The cost of stabilizing the financial system is likely to be significantly lower than previously expected," Geithner wrote in the letter to Democratic and Republican leaders in the House and Senate.
He said that the administration was estimating a year ago that the effort to support the financial system would cost more than $500 billion, or 3.5 percent of the total economy, as measured by the gross domestic product. He said the new lower estimate would be the equivalent of less than 1 percent of GDP.
He said because of the lower costs, the federal deficit and the total national debt will be lower than earlier projections. Administration officials said the costs could fall even further as it prepares updates to the bailout costs included in the budget Obama sent to Congress in early February.
In his letter, Geithner included some revised estimates that the administration had already released along with new projections in some areas.
The administration had already lowered the cost of the $700 billion bailout program, known as the Troubled Asset Relief Program, to $117 billion. That covers the losses from the auto, AIG and the mortgage foreclosure programs and earnings of up to $11 billion from several other programs under TARP.
In addition to the $117 billion in TARP losses, the administration is estimating losses of $85 billion from the support to Fannie Mae and Freddie Mac. Those two categories of losses would be offset by the $115 billion in earnings the administration expects will be realized from the Fed's support programs.