(Recasts, adds details from latest data)

NEW YORK, June 11 (Reuters) - The U.S. Federal Reserve’s balance sheet shrank in the latest week as banks borrowed less from the central bank, suggesting less stress on the financial system, Fed data released on Thursday showed.

Its book of assets and liabilities, while more twice the size than a year ago due its unprecedented bailout of the banking sector, contracted to the smallest level in three months.

The Fed’s balance sheet -- a broad gauge of its lending to the financial system -- shrank to $2.036 trillion on Wednesday from $2.062 trillion on June 3. It peaked at $2.179 trillion on April 22.

Much of the week’s decline came from less longer-term borrowing from banks, the latest Fed data showed.

Their daily borrowing at the Fed’s Term Auction Facility eased to $336.57 billion a day in the week ended June 10, down from a daily rate of $372.54 billion in the prior week.

Banks’ overnight borrowing at the Fed’s discount window fell too. Those direct loans averaged $119.61 billion per day in the week ended June 10, down from $126.05 billion per day in the previous week.

Some other Fed financings also declined on the week, signaling the availability of credit in the open market rather than a reliance on the Fed as a lender of last resort.

For example, the U.S. central bank’s Commercial Paper Funding Facility, which funds top-notch short-term corporate debt, totaled $138.44 billion on Wednesday, down from $142.64 billion a week earlier.

The Fed's credit extended to troubled insurer AIG AIG.N was valued at $43.13 billion on Wednesday, little changed from last week.

Its holdings of agency mortgage-backed securities were $427.42 billion on Wednesday versus 427.63 billion last week.

Earlier Thursday, the Fed reported a net purchase of $23.02 billion in mortgage bonds guaranteed by housing agencies Fannie Mae FNM.PFNM.N, Freddie Mac FRE.NFRE.P and the Government National Mortgage Association, or Ginnie Mae.

The Fed’s Term Asset-Backed Securities Loan Facility, or TALF, grew to $25.24 billion from $15.38 billion a week ago.

Earlier this year, the government introduced TALF with the goal to jump-start the securitization market, which has remained dormant since the collapse of Lehman Brothers last fall.

In the heyday of securitization, Wall Street packaged hundreds of billions of dollars worth of consumer, mortgage and business loans and sold them to investors as securities. Some analysts have blamed the huge sums of money raised from the bundling of high-risk loans for the credit crisis. (Reporting by Richard Leong; Editing by Dan Grebler)