Mr Kaspersky denies his business helped the Russian Federal Security Service (FSB) steal sophisticated malware developed by the US National Security Agency (NSA).
He acknowledged that it was "technically, a very possible scenario" his company's anti-virus had detected the NSA hacking tools after an employee stashed them on his home computer.
However, Mr Kaspersky stated that his company did not assist the FSB with espionage activities and that he did not believe the FSB had compromised Kaspersky Lab's network.
Kaspersky Lab's chief executive said he did not understand where the allegations could have originated from and criticised The Wall Street Journal and The New York Times for a lack of evidence in their reporting.
He added that the claims of his company's involvement with espionage had harmed his business in America, and that the company had issued legal warnings to media organisations outside of the US regarding the "false allegations".
How damaging the reports have been for Kaspersky "depends on the country", he told Sky News, admitting the company was "expecting the allegations to have a negative impact on the United States".
"It's not too much but unfortunately after all these stories we'll have negative growth in the United States. But in many other nations our business is growing," he added.
The company has denied that it is actively colluding with the FSB, and Eugene Kaspersky told Sky News that annual security audits at the company have found no breach of its network that would allow Kremlin operatives illicit access.
"We are absolutely sure that there's nothing wrong," he said, repeating that there was no evidence for the allegations at all.
The company has now announced a global transparency initiative in response to the allegations, aiming to win back the trust of those who believe it may pose a security risk to them.
The claims in the US have not been shared by the cybersecurity agencies in the UK and Germany.
In October, Germany's Federal Office for Information Security (BSI) told Reuters that it had no evidence to support the US media reports.
"There are no plans to warn against the use of Kaspersky products since the BSI has no evidence for misconduct by the company or weaknesses in its software," the agency said.
A spokesperson for the NCSC told Sky News: "Supply chain security is a complex problem and our advice is much more detailed than noting the name on the product or the country the vendor comes from."
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