The New York-based insurer made its biggest cash repayment yet on a bailout credit line with the Federal Reserve Bank of New York. AIG sent the Fed “nearly $4 billion,” AIG said Monday, after the company’s International Lease Finance unit sold $4.4 billion in bonds this month.

The move brings the amount the insurer owes on its 2008 taxpayer rescue under $100 billion for the first time. The government committed as much as $182 billion in the days and weeks following the collapse of Lehman Brothers to prop up AIG and keep the big banks from trading with it from imploding as well.

Since then, AIG has been trying to pay down the loans at a time when a weak economy is making bailouts politically toxic. Late last year the company swapped stakes in two big insurers for a $25 billion cut in the Fed credit line, which originally was $85 billion.

“This is continuing tangible evidence of AIG’s progress in repaying the American taxpayers,” said CEO Robert Benmosche (right). “AIG is getting stronger every day. We still have more work to do, but we will finish the job and make sure we repay the American taxpayers.”

The move will reduce the balance on AIG’s credit line with the Fed to $15 billion, AIG said. As of June 30, the insurer also owed $31 billion on borrowings from the so-called Maiden Lane companies that the Fed set up to facilitate the unwinding of its toxic derivatives books, $49 billion in Treasury preferred stock and $6 billion in interest on the Fed credit line.

Though there is still some doubt about AIG’s prospects as an independent entity without government support, the company has been embraced by yield-chasers in the credit markets and is said to be considering a bond offering of its own in coming weeks.

Hoping to show AIG can stand on its own feet, the Fed is trimming the size of the credit line. AIG said it has $30 billion available under the line, which expires three years from now.

AIG shares rose 1% early Monday to $35.65.