NEW YORK, March 21 | (Reuters) - The U.S. Federal Reserve's balance sheet grew to a record size in the latest week with more holdings of U.S. government debt, Fed data released on Thursday showed. The Fed's balance sheet, a broad gauge of its lending to the financial system, stood at $3.189 trillion on March 20, compared with $3.147 trillion on March 13. The Fed's holdings of Treasuries totaled $1.785 trillion as of Wednesday versus $1.770 trillion the previous week. The Fed's ownership of mortgage bonds guaranteed by Fannie Mae, Freddie Mac and the Government National Mortgage Association (Ginnie Mae) totaled $1.086 trillion on Wednesday, compared with $1.061 trillion the previous week. The Fed's holdings of debt issued by Fannie Mae, Freddie Mac and the Federal Home Loan Bank system was $72.42 billion versus $73.59 billion in the previous week. The Fed's overnight direct loans to credit-worthy banks via its discount window averaged $6 million a day, unchanged from the prior week.