Manny Encarnacion, 49, was arrested in New Delhi on March 11 after he arrived on a Lufthansa Airlines flight from New York, Deputy Commissioner of Police Airport Security M I Haider said.
"Three 9mm bullets were found in his baggage. He was booked under Arms Act," Haider said.
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Encarnacion was produced in court the very same day and was granted bail, police said.
US Embassy officials had visited Encarnacion to assist him.
He has been barred from leaving the country and is due to appear in court on April 17.
Encarnacion accidentally left the bullets in his bag when he was visiting India to meet his newly-wed wife Vida, an Iranian student, a report in the New York Post said.
Meanwhile, the New York Mayor Bill de Blasio today said he is "troubled" by the detention of the police official and hoped that he would be treated fairly by Indian officials.
"Obviously we want to know a lot more about what's going on," he said at a law enforcement event in New York when asked about the Encarnacion's case.
"But so far, from what I'm hearing, I'm troubled by it and I want to make sure we're providing support to him and make sure he's not being treated unfairly," de Blasio added.
New York Police Commissioner Bill Bratton said the department is "staying very engaged with that issue in India...We are certainly concerned for that officer and for his wife who's there with him in India at this time."
"But that's a process that's moving slowly in the India justice system ? but we're staying informed," he said.