"We have nothing to hide," Armstrong said in Visalia California, prior to the fifth stage of the Tour of California. "We have nothing to run from."
From SBS Cycling Central: Landis admits doping
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Instead Armstrong questioned whether Landis - who was stripped of his 2006 Tour de France title after a positive drug test - could be believed.
"It's our word against his word," Armstrong said . "I like our word. We like our credibility.
"With regards to the specific allegations, the specific claims, they're not even worth getting into it," he said. "I'm not going to waste my time or your time.
"I think history speaks for itself here," Armstrong said.
'Systematic doping'
On Thursday Landis admitted systematic doping and accused former teammate Armstrong of doing the same - and of schooling him in doping methods - in emails he sent to cycling officials and sponsors.
He claimed he and other US cyclists conducted blood transfusions, and used steroids and the synthetic blood booster erythropoietin (EPO).
Landis also claimed former teammate Armstrong explained the doping process to him.
"He and I had lengthy discussions about it on our training rides during which time he also explained to me the evolution of EPO testing and how transfusions were now necessary due to the inconvenience of the new test," Landis wrote.
Sports news site ESPN.com said Landis confirmed to them that he had sent the emails admitting the use of performance-enhancing drugs, saying he wanted to "clear my conscience".
'No feelings of guilt'
Speaking to ESPN, Landis admitted "misjudgments", but said he felt no guilt at having taken performance-enhancing drugs.
"I don't feel guilty at all about having doped," he added. "I did what I did because that's what we (cyclists) did and it was a choice I had to make after 10 years or 12 years of hard work to get there.
"My choices were, do it and see if I can win, or don't do it and I tell people I just don't want to do that, and I decided to do it."
Landis lost an appeal before the Court of Arbitration for Sport (CAS) which threw out his case in June 2008 and ordered him to pay US$100,000 in judicial costs to the US Anti-Doping Agency.
Landis' attempts to clear his name are believed to have cost him some US$2 million.
