WASHINGTON—A $40 billion lawsuit against the U.S. government for its crisis-era bailout of American International Group Inc. got under way in federal court Monday, with a lawyer for the insurer's shareholders accusing the government of unlawfully seizing a majority stake in the insurer.

Litigator David Boies called the deal a "grab" of a 79.9% equity stake at an "extortion interest rate" in an unlawful attempt to punish AIG's shareholders.

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