In a summary of the case in a search warrant, a Ministry of Interior investigator, E.A. Spirenkova, said Nginx’s popular software belonged to Rambler, a Russian internet and media holding company controlled by a state bank and a well-connected billionaire.

Both Mr. Sysoyev and Mr. Konovalov worked previously at Rambler, which, according to the investigator, has “exclusive rights” to the software they sold. A criminal conspiracy to steal the software, the investigator said, had defrauded Rambler of 51 million rubles, around $810,000.

In the face of the public outcry, Rambler executives disowned the criminal case.

Writing on Facebook, Igor Ashmanov, Rambler’s former chief executive, dismissed the claims of theft as “frivolous” and “not based on anything at all,” a view echoed by many others in Russia’s IT sector. A group of former Rambler employees issued a statement saying they were “ashamed” of their former employer, accusing it of “intimidating business and trying to increase its capitalization by commandeering and misappropriating.”

Assailed on social media and in the Russian press as a bullying behemoth bent on grabbing a share of the money paid by the American company, Rambler issued a statement on Monday insisting that it had played no role in initiating the criminal case against Nginx and wanted it stopped.

Disputes over intellectual property are a regular feature of the fiercely competitive IT sector around the world, but these are usually adjudicated by courts in civil proceedings. In Russia, such cases quickly escalate into criminal investigations featuring security officers waving guns. Powerful figures in business with connections to the Russian state often use the security forces to extort money or favors from weaker rivals.

Mr. Konovalov, one of the Nginx founders whose Moscow home was raided, denounced the police action in an interview with Meduza, a news portal, as a “typical racket. Simple as that.” He said the raids had been “professional and polite, if you exclude the fact that special forces agents were standing around with automatic weapons.” Contacted by The New York Times, he declined to comment about accusations that he and his partner, Mr. Sysoyev, had stolen Rambler’s intellectual property.

Rambler, in a statement issued after an emergency board meeting on Monday, blamed Lynwood Investments, a Cyprus-registered company controlled by billionaire Aleksandr L. Mamut, a major shareholder in Rambler, for the criminal case against Nginx.