Smith's call came a day after the four suspended players in the case had their sanctions overturned on appeal after an investigation led by ex-NFL commissioner Paul Tagliabue.
Jonathan Vilma, Scott Fujita, Will Smith and Anthony Hargrove were suspended in May after an NFL probe found them to have had leading roles in a program that gave players cash rewards for knocking opponents out of games from 2009-11.
Tagliabue backed the league's main findings on the bounty scheme but ruled that the players should not have been banned.
"First and foremost, they (the NFL) should say they're sorry because they've maligned the character of good players," Smith said in an interview with 'CBS This Morning' television show.
"And if they certainly believe that they are right, the one thing that (Commissioner) Roger Goodell could do is simply release the transcripts and we will all know the truth," he added.
"I think that the league has an obligation to search for the truth, and I believe that the truth is that there were no bounties put on other players," said Smith.
Tagliabue cleared former Saints linebacker Fujita, now with the Cleveland Browns and put the main blame for the affair with Saints coaching staff and executives.
Asked in an email from Reuters for a response to Smith's call, NFL spokesman Greg Aiello said he had no comment on the issue of releasing the transcripts.
Aiello said, however, that Tagliabue's report had been clear in its backing for the league's core findings on the affair.
"Mr. Tagliabue confirmed the findings of our investigation. He found the three players' conduct (Vilma, Smith and Hargrove) to be conduct detrimental, as Commissioner Goodell previously found, and he specifically upheld the finding that Mr. Vilma placed a bounty on Brett Favre."
Former Minnesota Vikings quarterback Favre was hurt during his team's defeat to the Saints in the 2009 NFC Championship game after receiving a series of hits, some of a questionable nature.
Smith said, though, that he considered the NFL investigation had been flawed.
"I'm certainly disappointed in the way in which they conducted an investigation because I now know having read and seen all of the testimony that there was certainly no evidence that the bounties existed.
"I was a prosecutor in this city for ten years. I understand how to do investigations, and the investigation that the league did was sloppy, the investigation that they did was more outcome-focused than frankly process-focused," he said.
- American Football
- Sports & Recreation
- Will Smith
- Jonathan Vilma