Mr Greenberg led AIG from 1967 until earlier this month
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The former head of US insurance giant AIG chose not to answer questions from regulators probing fraud claims when he appeared before them on Tuesday.
The US Securities and Exchange Commission (SEC) is investigating alleged fraud in a suspect 2000 deal between insurers AIG and General Re.
American International Group is accused of improperly recording the deal.
Maurice Greenberg can decline to testify under US law which protects people from self-incrimination.
His lawyer said his client needed more time to prepare.
'Cordial meeting'
Mr Greenberg, 79, chose not to answer questions from both the SEC and New York State Attorney General Eliot Spitzer during a 45 minute meeting on Tuesday.
"It was a quiet, cordial meeting," a spokesman for Mr Greenberg's legal team told Reuters afterwards.
AIG is accused of improperly recording the 2000 deal with General Re to falsely boost its accounts.
Last month AIG admitted for the first time that it had discovered improper documentation connected to the transaction.
Helping investigations
General Re, a unit of billionaire investor Warren Buffett's Berkshire Hathaway holding company, is not under investigation.
Mr Buffett was interviewed as a witness by Mr Spitzer and the SEC on Monday.
"I told them everything I know," he said.
Mr Greenberg stood down two weeks ago, after leading the company since 1967.
He is one of 12 former AIG directors who have received subpoenas from the SEC.