Vinod Moorjani, 45, is accused of saying “bomb hai” [there is a bomb] during a call with the authorities at Mumbai International Airport on Sunday.
But he says he was asking about the status of his “Bom-Del” flight. Mumbai was formerly known as Bombay.
Officials say Mr Moorjani made the call after becoming frustrated with delays.
Police believe he intended to disrupt outgoing flights so he would not miss his connection in Rome, the Press Trust of India reports.
An official told the news agency that he was travelling from Mumbai to Virginia with his wife and children.
“Before the operator could hear more from Moorjani, he hung up the call, after which the operator alerted her seniors, who informed the police”, the official added.
But Mr Moorjani, a businessman and CEO of a US company, says he hung up because of a disturbance on the phone line.
He has appeared in court charged with criminal intimidation and other offences. (Courtesy BBC)