Mr Clarke has dismissed reports in the Times and the Guardian that suggested British American Tobacco (BAT), of which he is non-executive deputy chairman, misled Parliament over cigarette smuggling.
But on Thursday, a Labour Party spokesman denied Mr Clarke's spin accusation.
'Completely untrue'
"For the record, Kenneth Clarke's claims that the Labour Party or Alastair Campbell were somehow responsible for the latest stories in the press about his links to the tobacco industry are completely untrue - as any of the journalists who wrote these stories would be able to point out," he said.
The Guardian reported on Wednesday that new evidence from a whistleblower suggested the firm has been using a Swiss subsidiary and bank account secretly to control a worldwide smuggling network.
The paper said this had been happening during Mr Clarke's tenure as deputy chairman.
As Mr Clarke went head-to-head against leadership rival Iain Duncan Smith on Wednesday's programme, he said: "These stories come from Millbank."
"I don't think Iain's people have anything to do with this rubbish."
Mr Clarke, who is not personally implicated in the claims, defended BAT's integrity when he gave evidence to a Commons health select committee last year.
Committee chairman David Hinchcliffe told the Times on Wednesday he was concerned BAT may have misled the committee's inquiry and said a further inquiry could be merited.
Later, Howard Stoate, a Labour member of the committee said its investigation into smuggling allegations should be reopened.
But Mr Clarke told Newsnight: "Alastair Campbell has produced a left-wing MP who is prepared to hint he will recall the [Commons health] select committee.
"I am flattered the Labour Party want to stop me winning this election."
Allegations denied
BAT spokesman Scott Hailstone told BBC News Online that the newspaper articles were politically driven and contained no new information from allegations raised 18 months ago.
"We do not smuggle, we do not condone smuggling and we do not collude with smugglers," he said.
Mr Duncan Smith, said his supporters had nothing to do with the allegations and they would not be part of his leadership campaign.
BAT and Mr Clarke were called to give evidence to the Commons health select committee in February 2000, after The Guardian published allegations that BAT had benefited from the smuggling of billions of cigarettes.
The Times says there is no evidence Mr Clarke had set out to mislead the inquiry, or had any knowledge of the alleged smuggling.
'Reputable company'
Earlier on Wednesday Mr Clarke said the timing blamed the allegations on the "more fanatic end of the anti-tobacco lobby who think that the leadership election is a good opportunity to give it a whirl".
"The more fanatic of Iain Duncan Smith's supporters in the press were also likely suspects, he said.
He repeated his select committee testimony that BAT was a "reputable company".
"There is nothing wrong with my continued assurance that BAT does not organise smuggling."
Mr Clarke, who believes adults have a right to choose whether they smoke, said he would be happy to forego the £100,000 a year from his BAT directorship if he won the leadership contest.