Williams (above), a certified SANS instructor who runs cyber security consultancy Rendition Infosec, said in an op-ed written for the Cyberscoop website that the FBI was known to be claiming to companies that Kaspersky was spying on behalf of Russia.
It was thus logical to assume that if the claims were true, Kaspersky Labs would have intercepted these conversations and shared them with Russian intelligence.
Williams referred to a recent op-ed in The New York Times written by Democrat Senator Jeanne Shaheeen in which, he said, she "makes the same tired and weak argument that Kaspersky has Russian intelligence ties and that classified assessments would allay any public doubts".
US moves against Kaspersky Lab have come in the wake of allegations that Russia interfered in the 2016 US presidential elections.
As iTWire reported, the FBI has begun briefing firms in the US private sector to give up use of Kaspersky products.
In July, the US government removed Kaspersky products from a list of approved software suppliers for two government-wide purchasing contracts.
And there have been reports that the US Senate is set to use a provision in the National Defence Authorisation Act to look at a ban on the company's software in all federal agencies.
Williams, who has weighed into the issue before this, said that protection of intelligence sources and methods was a standard reason given for withholding intelligence data from public consumption.
"But, if Kaspersky and Russian intelligence knows what the FBI is briefing to US companies, there are no sources and methods to protect," he wrote.
"The American public remain the only people unable to make an informed decision about whether or not to use Kaspersky. The FBI needs to educate the American people so they can make an informed decision about Kaspersky.
"It’s high time the bureau showed its cards or folded its hand."