In a letter to the USADA dated on Friday, attorney Timothy Herman said that while the athlete is willing to cooperate with the agency, its request to interview him in the next two weeks "cannot be accommodated."
Herman blamed pre-existing obligations.
The USADA set a February 6 deadline for Armstrong to fully cooperate in its investigation in return for a possible lifting of his lifetime ban from cycling, the agency's chief executive Travis Tygart said in an excerpt from an interview due to air on the CBS "60 Minutes" program on Sunday.
After years of denials, Armstrong confessed last week in an interview with Oprah Winfrey that he used performance-enhancing drugs to cheat his way to a record seven Tour de France wins.
The USADA last year stripped Armstrong of his titles and called him a "serial cheat."
In his letter, Herman raised questions about the role of the USADA in ridding cycling of performance-enhancing drugs. He noted that "professional cycling is and has been largely a European sport."
Herman applauded the International Cycling Union's announcement on Friday that it would work with the World Anti-Doping Agency in a broad probe into the use of drugs and rely on a "truth and reconciliation" process.
"As such, we would like to make sure we coordinate with the truth and reconciliation process to examine the culture of doping in cycling in the past and to clear the air so that cycling can move forward," Herman wrote.
On Wednesday USADA general counsel William Bock III sent Herman a letter saying that Armstrong's admissions to Winfrey "removed any possible impediment to his cooperation with USADA."
"Your client has a great deal of information that is needed to clean up cycling; the time has clearly come for him to sit down with USADA and provide detailed information under oath and on the record regarding his doping and all potential anti-doping rule violations of others of which he has knowledge," Bock wrote.
Armstrong, 41, said in his interview with Winfrey on her cable network OWN that the lifetime ban against him is like a "death penalty."
He added that he had no ambitions to return to professional cycling but would like to compete in sanctioned athletic events.