The department has said so far that it plans to purchase up to $10 billion of the securities, which have been battered in recent months by the soaring number of defaults on home mortgages as the housing industry undergoes its worst slump in decades.
Treasury Secretary Henry Paulson announced the program to buy mortgage-backed securities on Sept. 7 at the same time he announced the government was seizing control of mortgage giants Fannie Mae and Freddie Mac in a bid to stabilize the nation's troubled housing market.
Fannie and Freddie, two publicly traded companies, together hold or guarantee about half of the nation's mortgage loans.
Treasury spokeswoman Jennifer Zuccarelli said the selection of Barclays and State Street was not tied to a separate program that received approval from Congress on Friday that authorizes Treasury to spend up to $700 billion to buy up distressed mortgage-backed assets on the books of financial companies.
Zuccarelli said that Barclays and State Street had begun making purchases but she refused to say how much had been spent so far. She said the government would give an accounting of that amount in the Treasury Department's monthly report on the federal budget.