"The risk that the Russian government, whether acting on its own or in collaboration with Kaspersky, could capitalize on access provided by Kaspersky products to compromise federal information and information systems directly implicates USA national security". The firm has about 400 million customers worldwide.
But the company's founder said that while he lived in Moscow and his firm co-operated with Russian law enforcement on cyber-security, there were no deeper ties.
Mr Kaspersky told the BBC that the Trump administration's move to ban government agencies from using his products was an "uncomfortable situation".
"The risk that the Russian government, whether acting on its own or in collaboration with Kaspersky, could capitalize on access provided by Kaspersky products to compromise federal information and information systems directly implicates USA national security", it added.
The U.S. government action raised the question of whether those users should follow the U.S. government's lead.
"The department is concerned about the ties between certain Kaspersky officials and Russian intelligence and other government agencies", she said in a statement. Unless directed otherwise by DHS based on new information, agencies and departments have 90 days from the date of the directive to discontinue use of Kaspersky Lab products. Kaspersky products will now be withdrawn from stores and the firm's website. Last week, Best Buy Co, the No.1 US electronics retailer, said it was pulling Kaspersky Lab's cyber security products from its shelves and website.More news: Top House Tax Writer Says Overhaul Framework Coming Week of September 25
Best Buy was the first big retailer this month to announce it would stop selling the software.
The chief executive of the software company, Eugene Kaspersky, is a mathematical engineer who attended a KGB-sponsored school and once worked for Russia's Ministry of Defense.
In an email to Reuters, Kaspersky said, "I appreciate and accept the invitation to testify before the US House of Representatives Committee on Science, Space, and Technology, and if I can get an expedited visa, I look forward to publicly addressing the allegations about my company and its products".
Kaspersky Lab denies the allegations.
The government ban should alarm any company that has been relying on Kaspersky's software to protect its business, said Nate Fick, CEO of computer security specialist Endgame.
However, it may have an impact in terms of raising suspicion of the company and discouraging sales, especially following admissions that the United States government has been secretly briefing major U.S. companies to ditch Kaspersky software.