WASHINGTON — The Obama administration plans to cut its estimate of the projected costs of the government bailout program by at least $200 billion, a Treasury official said today. The August estimate was $341 billion.

The official, who spoke on condition of anonymity because the administration’s new projection has not been presented to Congress, said the reduced cost estimate reflected faster repayments by big banks and less spending on some of the programs.

The administration’s estimate that the $700 billion financial rescue program will cost at most $141 billion is down sharply from the estimate of $341 billion made in the administration’s mid-session budget review in August.

The official said the new estimate will become part of the administration’s new budget, which President Barack Obama will present to Congress in February.

The $700 billion financial rescue program, known as the Troubled Asset Relief Program, was passed by Congress in October 2008 at the height of the worst financial crisis to hit the country since the 1930s.

Obama is scheduled to give a speech on the economy Tuesday, and it is possible that he will raise the idea of using repaid TARP funds for increased efforts to help the unemployed.

Republicans have voiced opposition to this approach, arguing that the money should be used to lower the government’s ballooning deficits.

Treasury Secretary Timothy Geithner has told Congress he hopes to end the bailout program as soon as possible. He has indicated a preference for using a portion of the TARP resources to pay down the national debt, which is being pushed higher by record deficits.

Lowering the estimated cost of TARP will also lower the administration’s projections for budget deficits. The deficit for the 2009 budget year which ended in September hit a record $1.42 trillion and the administration in August projected a slightly higher deficit for the current year.

Banks have already repaid about $70 billion in support they have received from the bailout fund, and Bank of America recently announced it was returning the $45 billion in government support it had received.