"The legislature should take strong and decisive action to censure them and perhaps even expel them from office," Rendell said in a statement sent to The Inquirer editorial board and several other publications. He could not be reached for further comment Tuesday.
Rendell's remarks come as Kane continues to defend her decision to shut down the case, which was launched before she took office, without bringing any charges.
Though Kane has said she believes crimes were committed, she contends that the investigation was so poorly managed by her predecessors - and possibly tainted by racial targeting - that it would have been impossible to prosecute the case.
Kane said she now supports referring the matter to the Pennsylvania State Ethics Commission. Several state lawmakers have said they support legislative hearings on the case and a tightening of state ethics rules.
On Tuesday, Democratic State Sen. Anthony Williams of Philadelphia said he will introduce legislation to ban cash gifts to public officials from lobbyists or others seeking to influence them. Williams joins three of his Senate colleagues in pushing for such a ban.
Separately, the House Committee on Ethics appears poised to launch its own inquiry into the four legislators captured on tape accepting cash or money orders.
"With power comes responsibility," Williams said. "We must be more accountable to the taxpayers of Pennsylvania."
In his statement Tuesday, Rendell argued that prosecutors who launched the sting offered the investigation's key witness, undercover operative Tyron B. Ali, a deal so generous that it would have compromised his credibility in court.
Ali had been facing more 2,000 counts in a fraud case involving $430,000 in funds diverted from a state program intended to feed low-income children and seniors.
Rendell also questioned the deal's timing - made just months before Kane, a Democrat, took office in January 2013.
"Any experienced prosecutor knows that you don't agree to drop all charges pending against a key cooperating witness prior to trial," Rendell wrote.
The cooperation agreement with Ali was signed in November 2012 by Kane's predecessors, although it was Kane who formally dismissed the fraud case against Ali in sealed court papers last fall.
Kane's office said Tuesday that she initially "had no intention" of honoring the agreement with Ali, but agreed to do so after his lawyer successfully challenged her refusal to do in court.
Kane has made no secret of her distaste for what she has called "the deal of the century."
Prosecutors who ran the sting have defended the investigation and its tactics, and vehemently deny that they engaged in racial targeting. They say Kane faced a conflict - her former campaign manager, among other supporters, had had past dealings with Ali - and believe she should have recused herself from making decisions in the case.
The lead prosecutor in the case, Frank G. Fina, who now heads the public-corruption unit in the Philadelphia District Attorney's Office, has challenged Kane to a public debate. Kane told WHYY's Newsworks on Monday that she does not see any purpose to that.
Amid the heightened scrutiny, Kane has hired veteran lawyer Richard A. Sprague to represent her in possible defamation suits.
On Tuesday, Kane's office announced that her spokesman, Joe Peters, was leaving his job. In a statement, Kane did not say whether Peters had resigned or was fired. She said Peters was among a circle of senior staffers who are her friends and who came to work for her "for a finite period of time."
Peters could not be reached for comment.
In his statement, Rendell defended Kane against the suggestion that she shut down the investigation for political reasons, noting that just days before The Inquirer disclosed the aborted probe, her office charged Democratic State Sen. LeAnna Washington in a separate corruption case.
Washington's attorney, Henry E. Hockeimer Jr., questioned the timing of those charges.
In a letter to Kane earlier this month, Hockeimer suggested that there had been discussions with the Attorney General's Office about finding a resolution to Washington's case that did not include criminal charges.
The Philadelphia defense attorney noted that in defending herself in a story by The Inquirer about the aborted sting, Kane pointed to the charges against Washington as proof that she does not shy away from prosecuting Democrats.
In his letter, Hockeimer asked Kane to provide documentation of when her office first became aware of the Inquirer story.
"We believe we are entitled to this information in order to assess whether the nature and timing of the charges against Sen. Washington were motivated by any improper considerations," Hockeimer wrote.
Hockeimer declined to comment on the letter Tuesday.
The Attorney General's Office has said the news stories about the sting investigation played no role in the decision to bring charges against Washington, who is scheduled for a preliminary hearing in the case Wednesday.
In another development Tuesday, Tom Wolf, the front-runner for the Democratic nomination for governor, criticized Kane's handling of the sting. He said it was inconceivable that legislators taking envelopes of cash could escape prosecution.
"What we've seen over the past week is unacceptable," Wolf said during an editorial board meeting with the news organization PennLive in Harrisburg. "People want their government to run according to certain high ethical standards, and that's not what we've seen."
Wolf's four opponents - Rob McCord, Kathleen McGinty, Allyson Schwartz, and Jack Wagner - declined in a joint forum Sunday in Philadelphia to second-guess Kane's actions. Wolf, who was campaigning in Pittsburgh, did not attend.
Asked Tuesday about Kane's decisions in the sting case, Wolf said: "If the investigation was proceeding down a bad path, put it on the right path."
Inquirer staff writer Thomas Fitzgerald contributed to this article.