The decision could help pave the way for generic competitors of Teva's Copaxone drug to go on the market as soon as next month.
Teva had sought to prevent the lower-court ruling from going into effect while the Supreme Court considers its appeal in the patent fight.
At issue is a July 2013 ruling by the U.S. Court of Appeals for the Federal Circuit in favor of two teams developing cheaper generic forms of Copaxone: one comprising Novartis AG's Sandoz Inc and Momenta Pharmaceuticals Inc, and the other comprising Mylan Inc and Natco Pharma Ltd.
In his decision on Friday, Roberts, in a brief opinion, wrote that he was not convinced Teva had shown the "likelihood of irreparable harm" if the application was denied, because if Teva wins the Supreme Court case it can seek damages from the generic companies for past infringement on its patents.
Teva still has the option of asking another justice for a stay, but such requests are rarely granted.
The appeals court upheld some of the nine patents involved in Copaxone, or portions of them, but declared several invalid, meaning patent protections were set to expire in May 2014 instead of September 2015. The outcome of the legal fight therefore determines how soon the generic drugs can go on sale.
The Supreme Court will not hear oral arguments in the Teva case until its 2014 term begins in October. A ruling could come as late as June 2015, which is why Teva sought to stay the lower court decision.
The case is Teva v. Sandoz, U.S. Supreme Court, 13-854.