The King County Prosecuting Attorney's Office determined there was insufficient evidence to support any criminal charge, spokesman Dan Donohoe said Thursday.
Saleem was arrested Monday night after his family reportedly got into a heated argument near the baggage claim. Some relatives told police that he threatened to kill them.
The mayor on Thursday said he never threatened or assaulted anyone.
Saleem said he was unhappy with how Port of Seattle police and King County Jail staff handled the incident. He believes he should not have been arrested.
"Me and my family, we want to put this behind us and get on with our lives," he said. "It's going to be very difficult because my reputation has been damaged, but it is what it is and we want to move forward."
Saleem was at the airport to pick up his daughter, 13.
She and other relatives were flying back from California on Monday after a vacation in California, court papers show. The family had been quarreling during the vacation, and the argument apparently continued into the airport. Port police responded to reports of a commotion.
Because of the nature of the incident, state law mandated Saleem's arrest, a police spokesman said earlier this week.
Saleem was booked into the King County Jail late Monday night for investigation of felony domestic-violence harassment. He was released from jail Tuesday morning without having to post bail.
Saleem said he is grateful for people who have supported him these past few days.
He also said he wanted to apologize to the Granite Falls community for any backlash the town may have suffered.
"I am back, and I am going to attend to the business of the city, and I am going to do everything I possibly can to do what is best for the city in the future," he said.
Rikki King: 425-339-3449; firstname.lastname@example.org.
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