Andrew Cuomo said he hoped to recoup $80m (£55m) of bonus payments - which amounts to about half of the $165 million paid by AIG on 15 March.
The US rescued AIG with bail-out funds totalling $170bn since September 2008.
Treasury Secretary Timothy Geithner is due to testify on Tuesday on the need to reform the US financial system.
He said on Monday that the banking crisis showed the country's financial regulatory system had failed and needed to be replaced by a stronger system with a better regulations.
"Our system basically failed its most fundamental test," he said in remarks before he was due to appear before the House of Representatives Financial Services Committee on Tuesday. "It was too fragile."
Bonus tax?
AIG's decision to pay bonuses despite being bailed out by the government had sparked widespread outrage in the US.
Ranked the 18th biggest company in the world by Forbes at the start of 2008, it suffered massive losses related to the problems afflicting the housing and credit markets.
AIG played a key role in insuring risk for financial institutions around the world.
The troubled insurer reported a loss of $61.7bn for the last three months of 2008, the biggest quarterly loss in corporate history.
The bonus debacle had prompted the approval of a bill by the US House of Representatives to impose a 90% tax on bonuses awarded by companies bailed out by the US government.
But President Barack Obama said such a measure would be unconstitutional.
The announcement that much of that money is now being returned seems likely to ensure that the bill never reaches his desk, says the BBC's Richard Lister in Washington.
Mr Cuomo said 15 of AIG's top 20 bonus recipients had agreed to return their payments, which he estimated to total around $30m.
"A number of them have risen to the occasion and I applaud them," Mr Cuomo - who is investigating AIG as well as several other financial institutions - said of the executives who had offered to give up their bonuses.
He added that he expected to recoup all of the bonuses paid to American citizens working for AIG, which accounts for around half the $165m the company paid out.
Mr Cuomo said he did not plan to release the names of the employees who have agreed to return the bonuses, suggesting there was no implied threat that if an employee refused to return their bonus, their name would be disclosed.
Bonuses ranging from $1,000 to more than $6m were paid to some 400 staff in the division handling the mortgage-backed assets at the heart of the financial crisis.
Seven senior employees were paid more than $3 million, while 73 members of staff received bonuses of more than $1m.
