He pleaded not guilty to all 13 counts and agreed to bail of $500,000 (£400,000). He is not due to appear in court again until 30 June.
Having surrendered his passport and given addresses in Queens and Washington DC, he was told he was allowed to travel to Long Island, New York City and Washington. Travel elsewhere will require notice.
Santos's attorney, Joseph Murray, told the Guardian: "He is definitely running for re-election. He is planning to go back to work."
Santos had surrendered at the courthouse in Central Islip, Long Island, a day after he was informed of the indictment, slipping in through a back door.
The US justice department unsealed an indictment consisting of seven counts of wire fraud, three counts of money laundering, one count of theft of public money and two counts of making false statements in reports to the House.
Santos faces a maximum sentence of 20 years on the top count, the US attorney's office for the eastern district of New York said. He will not have to relinquish his congressional seat, although members sentenced to at least two years cannot vote or be on committees.
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