In the letter to TSA director Edmund "Kip" Hawley, Thompson said he is talking to a growing number of TSA workers in Jackson who are fearful they may lose their jobs for blowing the whistle on security problems at the airport.
TSA investigators came to Jackson last month to look into claims by current and former workers that TSA management used inside information to cheat undercover tests of security procedures.
The alleged security breaches were outlined in a story in The Clarion-Ledger following a two-month investigation.
The workers also said attitudes toward federal security regulations were so lax that dangerous items sometimes were allowed to pass through into supposedly secure areas of the airport.
But Thompson said he has learned that only selected employees were interviewed by the investigators and the interviews often were held in rooms adjoining the offices of Federal Security Director Larry Rowlett and other top TSA managers.
In a letter last month to Hawley, Thompson called for Rowlett to be put on administrative leave for the duration of the investigation to make sure employees could speak without fear of reprisals.
TSA officials instead issued a statement of support for Rowlett, citing his long career in federal service, including a stint as chief Secret Service agent for Mississippi.
"The (TSA) Office of Investigations will never get to the bottom of the problems at Jackson if Mr. Rowlett and his management team are able to keep their ears to the keyhole and eyes on the door," Thompson wrote.
TSA spokeswoman Sari Koshetz would not comment on the letter on the grounds that it involved "personnel issues." TSA also offered no comment on whether investigators were able to substantiate the claims made by current and former TSA employees.
In earlier statements, TSA spokespersons have denied any dangerous items have made it past security checkpoints and suggested that any warnings of upcoming tests were the result of workers at one airport gossiping with screeners in Jackson.
Bill Gillam, a former TSA screener, said he was interviewed away from the airport by two investigators.
Gillam and others claim that TSA management would brief workers before supposedly secret tests where undercover agents - known as "red teams" - would attempt to sneak dangerous items into the airport.
Gillam said he provided a list of names of other workers willing to be interviewed under oath about airport operations.
"There are some people who want to know why they have not been interviewed," he said.
One TSA worker said he does not believe the promise of confidentiality was entirely kept.
He said his confidence in the investigation is "extremely low."
The worker would not go on the record for fear of retaliation.
Many workers with legitimate complaints about the management of airport security were not interviewed, he said.
"It has all the appearance of another TSA whitewash. I don't have any confidence in what TSA does for that reason," he said.
Thompson said he does not want that to happen.
"I've assured everybody concerned that, to the extent I can get the department to do a thorough and unbiased investigation, I will do that," he said.
Claims of security problems at the airport are not new.
In January, TSA officials in Washington told their Jackson counterparts that Jackson Mayor Frank Melton was no longer allowed to bring his personal firearms aboard commercial flights leaving the airport.
Melton had flown armed several times since becoming mayor last year by showing a badge and a letter signed by Police Chief Shirlene Anderson.