She added that she will leave the safety issues "up to the professionals at the corporate level at Allegiant and hope they are as concerned about safety as much as we are".
On Sunday evening, CBS "60 minutes" aired a scathing report, which found that Allegiant Air's planes had three times as many mechanical problems with flights as six competing airlines between January 2017 and October 2017.
Shares of Allegiant fell almost 9% dive on Friday, and shares fell another 2% in Monday.
Canadian global affairs analyst and former aviation journalist Michael Bociurkiw said it's "absolutely shocking" that the U.S. Federal Aviation Administration hasn't taken action against Allegiant, given the number of mechanical problems the airline's fleet has allegedly experienced.
But FAA officials have said they are vigilant monitoring safety efforts at all airlines, and found no systemic problems at Allegiant.
Robert Kane, left, and Sean Jenks of Port City Air refuel an Allegiant Air passenger jet during a turnaround at Portsmouth International Airport at Pease in 2016.
On Monday, Allegiant issued a statement by Eric Gust, vice president of operations, charging that the CBS story told a "false narrative" about Allegiant and the FAA.
In earnings calls, analysts have pressed the publicly traded airline about the rising costs of maintaining its MD-80s, including the loss of revenue when the planes are out of service for increasingly frequent repairs.More news: Rain postpones Food City 500 finale until Monday
"I just heard my friends say they are always late, and people don't treat them right on the plane", traveler Abigail Vega said.
In Sunday's episode of "60 Minutes", CBS Correspondent Steve Kroft shared his extensive investigation into the Las Vegas-based low-budget airline Allegiant Air.
Whitmer said earlier that Allegiant has carried more than 350,000 passengers out of Owensboro since 2009.
This approach has allowed Allegiant to thrive at secondary airports such as Stewart where there isn't a natural or substantial business-travel market. To infer that any one of the professionals at Allegiant would fly anything less than a safe aircraft is appalling and insulting.
Allegiant service means $1 million a year to the local airport, because it carries more than 10,000 passengers a year on the Florida route.
The FAA increased its monitoring of Allegiant in 2016 because of labor tension with its pilots.
US Representative Charlie Crist, a Florida Democrat, wrote separately to the Transportation Department, demanding the agency "take action to improve passenger safety", as well as to hold Allegiant accountable for past safety failures. But as "60 Minutes" reported, when a near crash happened due to a missing component in 2015, the FAA investigator recommended strong enforcement and maximum fines. The company, which now has around 100 planes in its fleet, has seen 25 of its planes experience major failures in the last two years alone.