* FSOC voted on Friday to remove AIG's 'systemically risky' label

* Yellen swung vote; three other Obama-appointees vote against

* Fellow insurer Prudential is also hoping to shake-off SIFI label

By Michelle Price

WASHINGTON, Oct 2 (Reuters) - American International Group's poses less of a threat to financial stability because it shrank its assets by more than $500 billion, Federal Reserve chair Janet Yellen said on Monday in explaining a regulatory council's decision to release the company from stricter oversight.

Her comments, published by the Fed in a statement, shed light on a regulatory process financial firms say is too opaque and unaccountable, indicating big banks and insurers will have to downsize dramatically if they are to shake-off the "systemically risky" label.

The U.S. Financial Stability Oversight Council (FSOC) determined on Friday that AIG - which received a $182 billion U.S. government bailout during the 2007-2009 global financial crisis - is no longer critical to the health of the U.S. financial system. "Since the financial crisis, AIG has largely sold off or wound down its capital markets businesses, and has become a smaller firm that poses less of a threat to financial stability," Yellen said in the statement.

"It is important to continue to monitor large nonbank financial firms to ensure that, should they encounter distress, the functioning of the broader economy is not threatened. The possibility of de-designation provides an incentive for designated firms to significantly reduce their systemic footprint," she added.

The FSOC, which comprises the heads of financial regulators across the government, requires a two-thirds majority to agree to remove a company’s designation as a “systemically important financial institution” or SIFI.

With four appointees of President Barack Obama still holding FSOC seats, Yellen's vote proved decisive on Friday. The remaining three Obama appointees voted against while four Trump appointees voted in favor, Treasury documents showed.

By law, all banks with over $50 billion in assets are automatically considered SIFIs, while the FSOC can apply the label to nonbanks on a case-by-case basis. The panel only once before has removed a SIFI designation with GE Capital in 2016.

The FSOC’s Friday decision left fellow insurer Prudential as the only remaining nonbank SIFI. The company said in a statement it was "encouraged" by AIG's removal from the SIFI list and would continue to contest its designation.

In April, Republican President Donald Trump ordered a review of the SIFI designation process, raising banks' hopes more firms may ultimately be removed from the list.