U.S. District Judge Robert Wilkins in Washington, D.C., said the complaints brought by the government and Armstrong's former teammate Floyd Landis were "rife with allegations that Armstrong had knowledge of the doping, and that he made false statements to conceal the doping and the attendant obligation which would have resulted if the government had known of the doping."
Armstrong, 42, was stripped of his seven victories at the Tour de France and banned for life in 2012 by the U.S. Anti-Doping Agency after it accused him in a report of engineering one of the most sophisticated doping schemes in sports.
Armstrong admitted in January 2013 to doping, and faces several civil lawsuits that could drain the cancer survivor's wealth accumulated when he was among the world's most popular and successful athletes.
Damages in the case before Wilkins could top $100 million, court papers show.
Robert Luskin and Elliot Peters, two of Armstrong's lawyers, did not immediately respond to requests for comment.
They have argued that the Postal Service benefited from the valuable exposure it got from its sponsorship, and that the lawsuit had been brought too late.
Paul Scott, a lawyer for Landis, did not immediately respond to a request for comment. U.S. Department of Justice spokesman Peter Carr declined to comment.
Landis, who lied about his own doping before confessing, originally brought the lawsuit in 2010 under a federal law, the False Claims Act, that lets whistleblowers pursue fraud cases on behalf of the government, and obtain rewards if successful.
The Justice Department joined the case in February 2013, hoping to recover some of the estimated $40.5 million that the Postal Service paid from 1998 to 2004 to have Armstrong and his teammates from the now-defunct Tailwind Sports Corp wear its logo during races.
Court papers submitted by Armstrong's lawyers this month show the government has been seeking to recoup more than $105 million from Armstrong, Tailwind and former team manager Johan Bruyneel.
This sum reflected triple damages under the False Claims Act for claims made after June 10, 2000, which was 10 years before the lawsuit began, the papers show.
In Thursday's decision, Wilkins also denied Bruyneel's request to dismiss the lawsuits against him.
Rebecca Worthington, a lawyer for Bruyneel, was not immediately available for comment.
The case is Landis v. Tailwind Sports Corp et al, U.S. District Court, District of Columbia, No. 10-00976.