The former cyclist said his attempts to destroy team masseuse Emma O'Reilly's reputation were "inexcusable and embarrassing".
Armstrong has walked to the border of truth many times before but has yet to cross it; now he smells a chance at a reduced ban from sport.
Sir Bradley Wiggins said it was "emotional" watching Lance Armstrong admit to using performance-enhancing drugs.
The Livestrong Foundation, the cancer charity founded by disgraced cyclist Lance Armstrong, said that Nike had dropped its sponsorship of the group, which is known for its distinctive yellow wristbands.
The group had flourished during Armstrong's cycling career, which saw him win the grueling Tour de France race seven times, titles he was stripped of last year amid accusations that he used performance-enhancing drugs.
Armstrong admitted to doping early this year and stepped aside from the charity, which he had founded after being diagnosed with testicular cancer.
"We expected and planned for changes like this and are therefore in a good position to adjust swiftly and move forward with our patient-focused work," the group said in a statement.
US Masters Swimming Executive Director Rob Butcher confirmed that disgraced cyclist Lance Armstrong has pulled out three events he was scheduled to appear in this weekend.
Butcher told the Associated Press that the change of heart was likely caused by objections raised by FINA, the international governing body for swimming.
He doesn't want to cause any more harm to any more organisations. His interest was around fitness and training. In light of FINA and the other political stuff, he will not be swimming.
Lance Armstrong has pulled out of the swimming competition he was due to take part in this weekend in Austin, Texas, Sky News report.
FINA, the international governing body for swimming, has written to the US Masters Swimming to advise them to reject Lance Armstrong's entry to take part in a competition scheduled this weekend.
The disgraced cyclist was planning to use the small low-profile event in Austin, Texas, to make a return to competitive sport.
The competition falls under the jurisdiction of the US Masters Swimming. In a statement, the governing body said:
FINA wrote a letter to the US Masters Swimming (with copy to US Aquatic Sports and USA Swimming) requesting not to accept the entry of Mr. Lance Armstrong in the [...] competition.
Lance Armstrong's return to competitive sport this weekend will be against veteran swimmers, a Texas newspaper reported.
Most competitors in the US Masters Swimming event entered by Armstrong will be older than the 41-year-old cyclist, the Austin American-Statesman said.
Armstrong is banned for life from all competitions that adhere to world anti-doping codes, but is allowed to take part in the low-profile Austin swimming event.
US Masters Swimming executive director Rob Butcher said nobody had raised formal objections to Armstrong competing.
Butcher added: "The purpose of our organisation is to encourage adults to swim."
Lance Armstrong is planning to make a return to competitive sport as a swimmer this weekend.
The disgraced American cyclist is entered for the Masters South Central Zone Swimming Championships, which takes place at the University of Texas.
Armstrong is set to compete in freestyle races over 500 yards, 1,000 yards and 1,650 yards at the event in his home city of Austin.
Armstrong was stripped of his seven Tour de France titles last year for being part of a doping scandal.
Lance Armstrong's lawyer says that the Justice Department has joined a fraud lawsuit against the disgraced cyclist.
The US Anti-Doping Agency has claimed that Lance Armstrong "was worried of potential criminal and civil liability" if he gave evidence to them about doping:
We have provided Mr Armstrong several opportunities to assist in our ongoing efforts to clean up the sport of cycling.
Following his recent television interview, we again invited him to come in and provide honest information, and he was informed in writing by the World Anti-Doping Agency (WADA) that this was the appropriate avenue for him if he wanted to be part of the solution.
– US Anti-Doping Agency chief executive Travis Tygart
Over the last few weeks he has led us to believe that he wanted to come in and assist USADA, but was worried of potential criminal and civil liability if he did so.
Today we learned from the media that Mr Armstrong is choosing not to come in and be truthful and that he will not take the opportunity to work toward righting his wrongs in sport.
Lance Armstrong's lawyer has said the cyclist will not be interviewed under oath by a U.S. Anti-Doping Agency official who wanted him to tell them all he knows about doping:
Lance is willing to cooperate fully and has been very clear: He will be the first man through the door, and once inside will answer every question, at an international tribunal formed to comprehensively address pro cycling, an almost exclusively European sport.
We remain hopeful that an international effort will be mounted, and we will do everything we can to facilitate that result.
– Lance Armstrong's lawyer Tim Herman
In the meantime, for several reasons, Lance will not participate in USADA's efforts to selectively conduct American prosecutions that only demonise selected individuals while failing to address the 95% of the sport over which USADA has no jurisdiction.
Lance Armstrong's lawyer has said the cyclist won't be interviewed under oath by a U.S. Anti-Doping Agency official who wanted him to tell them all he knows about doping, according to the AP news agency.
USADA officials had said the disgraced cyclist must speak with them if he hoped to reduce his lifetime ban from sports. Today was the deadline for him to agree to speak to them.
Tim Herman said the process served "only to demonise selected individuals."