Coulter had tweeted that Delta on Saturday, apparently following her flight to West Palm Beach from La Guardia airport in NY, was the worst airline in the U.S.
She joked that Delta hires people who seek to be prison guards, animal handlers or East German police.
Coulter posted a photo Saturday of the passenger she said was in the seat for which she paid extra in advance.
"Additionally, your insults about our other customers and employees are unacceptable and unnecessary", Delta added in a follow-up tweet.
She then detailed how she had been asked to move from the seat she had with additional leg room that she carefully had picked ahead of time and booked, posting a photo of the seat and the woman who was given it, and targeting the employees at Delta. "We are aware of the customer's comment and we're reaching out directly to her to address the complaint", he said.
"$30! It cost me $10,000 of my time to pre-select the seat I wanted, investigate type of plane & go back periodically to review seat options", she tweeted Saturday evening. She also quipped that Delta's motto is: "How can we make your flight more uncomfortable?"
Gillian Brockell, a former flight attendant, defended Delta when she wrote: "I can say there are a lot of "emergency" reasons to put a family together".
Delta expects mutual civility throughout the entire travel experience. The airline said a flight attendant had stepped in to deal with "confusion" arising from the seat reassignment and that "all customers complied and the flight departed without incident".
Coulter's tweets generated a fair amount of support from others on social media, with some of her backers saying they would not fly with the US airline.
Despite the airline's indignation at Coulter's disparaging remarks, she launched a second tirade in the early hours of Monday morning.