The prosecutors on Friday asked to postpone the hearing for one of the firms implicated in the case, Concord Management and Consulting.
The judge did not explain why she rejected the request to delay an arraignment scheduled for May 9, Politico news outlet reported on Saturday.
Mueller's team said Friday that the lawyers for Concord had asked to disclose various information on the case. The defendants have used their right to legal discovery to demand details of electronic surveillance by US intelligence, identities of informants, and other information.
Mueller is heading the investigation into the alleged Russia's attempt to influence the outcome of the 2016 US presidential election. Similar probes are being carried out in the Senate and the House of Representatives.
Russian officials have repeatedly refuted the accusations and stressed that the allegations of Moscow's involvement remain unfounded.