Mr Kaspersky told the BBC that the Trump administration's move to ban government agencies from using his products was an "uncomfortable situation". The US has said it is concerned that Kaspersky is vulnerable to influence from the Kremlin.

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.

"When they say we have strong ties with Russian espionage it's not true," he told me via a video call from Argentina.

"We co-operate with many law enforcement agencies around the world - in the past with the US as well."

'Unfair competition'

The American store chain Best Buy has stopped selling Kaspersky products, but Mr Kaspersky said he had had positive discussions with other retailers.

The Kremlin has criticised the US government's actions, describing the ban as unfair competition.

Eugene Kaspersky said he wanted relations between the two countries to improve and called for international co-operation on cyber-security - he insisted that "only the bad guys are happy with this situation".

The problem for the company is that Russia is now seen as a haven for hackers and cyber-criminals, and its government is widely accepted to have interfered in last year's American presidential election.

That means that a Russian business offering cyber-security software may struggle to convince American consumers to buy products that their own government suggests are unsafe.

But Mr Kaspersky said the Americans could have full access to his company's activities: "We will open every door, check everything. We don't have any secrets, we don't do anything bad against our customers and against governments."

While he described the revenue his firm earns from the US government as "close to zero", the wider US market accounts for about a quarter of Kaspersky's sales.

He had this appeal to his American customers: "Please stay with us - you can trust us."