After urging the World Anti-Doping Agency to introduce tougher punishments for drug cheats, Bach told The Associated Press in an interview that Armstrong has not made a "real admission" and his ban should not be reviewed.
Armstrong has suggested he might co-operate with a cycling commission investigating doping in return for a reduction in his life ban from all organized sport. Speculation has increased after WADA said Tuesday an independent cycling investigation was imminent.
"I would not feel comfortable with this (reducing Armstrong's ban) because it is too little, too late. It was not even a real admission," Bach told the AP after addressing delegates at the World Conference on Doping in Sport.
"Now trying to bargain a deal there after everything has been proven, and now that he realizes he doesn't just get off the hook — this is not the best way, to lessen a sanction or to be lenient there in any way," he added.
Bach supported cycling's move toward an open process with regard to its drug-stained past. Cycling and its dark doping history has become a key behind-the-scenes issue at the conference.
Bach told the AP he will meet with Brian Cookson, the new head of cycling governing body UCI, on Wednesday or Thursday in Johannesburg. The UCI has approached the IOC to "consult" on some of its doping issues, Bach said.
"I think cycling is taking the opportunity to strengthen their fight against doping," Bach said. "What I have seen and heard so far is that the UCI is really going in the right direction."
On a separate issue, Bach questioned whether traditional blood and urine tests were still the best way to catch doping cheats.
WADA is expected to re-examine some of its testing procedures in the wake of a report this year that testing had been generally unsuccessful, underlined by the fact that Armstrong never failed a test.
"Is it not time to find out, for example, whether blood and urine tests are really the best and ultimate solution?" Bach asked delegates. "Might there be other testing methods, which are even more reliable, more sustainable, more effective, and maybe even less intrusive?"
Bach, who was elected to succeed Jacques Rogge in September, voiced his support for doubling the standard suspension for serious doping violations from two years to four.
WADA is expected to approve the move to four-year bans later this week along with other revisions to the international anti-doping code. The new code will come into effect on Jan. 1, 2015 and in time for the next Summer Olympics in Rio de Janeiro in 2016.
The four-year bans will ensure doping violators miss at least one Olympics, an important factor for Bach. A previous IOC rule to that effect was thrown out by the Court of Arbitration for Sport because it wasn't included in the WADA code.
"It adds to the deterring factor of the sanction because until now there was something in between, they could still come back at the next edition of the games," Bach said. "And some may even have calculated with this comeback and therefore it is a very important step forward."
Bach said he once supported lifetime bans for a first offence, a move that has been ruled out because of human rights issues. Lawyers advised Bach that lifetime bans for first offences wouldn't be possible.
"It is a pity but you have to expect this," Bach said.
In his speech to the conference, Bach said the 2014 Winter Olympics in Sochi, Russia, will be the most drug-tested in Winter Games history.
There will be 1,269 pre-competition tests ahead of the games, up from 804 at the 2010 Vancouver Games. There will be a total of 2,453 tests around the games, up from 2,149 four years ago. The IOC will spend $1 million on pre-competition testing for Sochi and "many millions" on testing throughout the Feb. 7-23 games.
"To be clear ... To be very clear. These millions of dollars are not expenses. They are an investment in the future of our sports," Bach said.
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