"This action is based on the information security risks presented by the use of Kaspersky products on federal information systems", the statement from the DHS said.
Kaspersky has been in the spotlight for months over allegations of ties between the company and Russian intelligence.
The Reuters news agency cited the U.S. House Committee on Science, Space and Technology as saying on Thursday that it had invited Eugene Kaspersky to testify on September 27. alongside an unspecified number of U.S. government and private sector cyber experts.
Duke directed all USA federal agencies and departments to stop using products or services supplied directly or indirectly by the Russian-owned and operated company.
The invitation came a day after the Trump administration told United States government agencies to remove Kaspersky Lab products from their networks, saying it was concerned the company was vulnerable to Russian government influence and that using its anti-virus software could jeopardise national security.
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Kaspersky cited "geopolitical turbulence" as the likely reason why U.S. Homeland Security banned his company's products from federal IT systems. The US government believes the antivirus firm has been colluding with the Russian government.
But Mr Kaspersky said the Americans could have full access to his company's activities: "We will open every door, check everything".
Russian hackers are believed to be responsible for a significant proportion of global cyber-crime, and many people in the security community believe that Russian law enforcement agencies turn a blind eye to their activies as long as they are carried out overseas. According to current and former American officials, the Federal Bureau of Investigation working with American spies have been trying to determine for years whether or not executives at Kaspersky are working with Russian military or intelligence agencies. It said Thursday that it will continue to get its product to customers "through its website and other prominent retailers". 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. The retail giant Best Buy has said it would stop selling the company's software.
The company denied the allegations.
During a Senate hearing in May, American security officials including the chiefs of the Federal Bureau of Investigation and Central Intelligence Agency were asked if they were comfortable having Kaspersky software running on their organizations' computers. Democratic Sen. Jeanne Shaheen of New Hampshire has push legislation that would ban the company's products governmentwide. The FBI warned industry leaders about potential risks of using Kaspersky products a year ago.