WASHINGTON — A group of federal regulators voted Friday to no longer classify the American International Group as “too big to fail,” freeing the giant insurer from years of tough government oversight.

The vote came nine years after the government rescued A.I.G. in a significant bailout at the height of the financial crisis, making the insurance company a symbol of the financial industry’s recklessness.

Since nearly collapsing in September 2008, A.I.G. has sold off numerous business lines and significantly revamped its operations. It also repaid the $182 billion in bailout money it received from the government.

In an effort to prevent a repeat of the crisis, the Dodd-Frank law of 2010 empowered regulators to designate certain nonbank financial institutions as “systemically important” and subject them to more intensive supervision. A.I.G. and other companies that received the label have fought to shed it, arguing that they aren’t big or interconnected enough to imperil the broader financial system if they run into problems.