The shooting victim, Michael Winchester, 52, was the father of football player James Winchester, a long snapper for the Kansas City Chiefs.
The shooting appeared to have been premeditated, Oklahoma City Police Captain Paco Balderrama told a news conference, but authorities did not disclose a motive and said the suspect has not yet been positively identified.
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The shooting occurred in a parking lot at Will Rogers World Airport around 1 pm, Balderrama said.
He said the suspect was found dead inside his truck in an airport parking garage.
Ken Sarnoff, the agent for James Winchester, announced the death of the player's father in a Twitter posting.
"Our love and support is with James and the entire Winchester family," the Kansas City Chiefs said in a statement released later.
Will Rogers World Airport officials said on Twitter that the airport was "slowly resuming" operations. Airport spokesperson Karen Carney said about 25 flights were canceled on Tuesday.
Most of the cancellations were from Southwest, which said it had canceled all inbound and outbound flights for the remainder of the day, Carney said.
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Police armed with rifles swept through the airport parking lot in their search. Police said they expected the airport to be fully operational by Wednesday.
Balderrama said travelers who had to remain on airport property as police searched the area were being allowed to leave by Tuesday evening.
The airport is the main commercial air hub for Oklahoma City and services an average of 150 flights a day, the airport said.
"We extend our heartfelt sympathies and support to his family and Southwest co-workers at this time," Southwest said in a statement.
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