British website owners could face extradition to the US on piracy charges even if their operation has no connection to America and does something which is most probably legal in the UK, the official leading US web anti-piracy efforts has told the Guardian.

The US's Immigration and Customs Enforcement agency (ICE) is targeting overseas websites it believes are breaking US copyrights whether or not their servers are based in America or there is another direct US link, said Erik Barnett, the agency's assistant deputy director.

As long as a website's address ends in .com or .net, if it is implicated in the spread of pirated US-made films, TV or other media it is a legitimate target to be closed down or targeted for prosecution, Barnett said. While these web addresses are traditionally seen as global, all their connections are routed through Verisign, an internet infrastructure company based in Virginia, which the agency believes is sufficient to seek a US prosecution.

As well as sites that directly host or stream pirated material, ICE is also focusing on those that simply provide links to it elsewhere. There remains considerable doubt as to whether this is even illegal in Britain – the only such case to be heard before a British court, involving a site called TV-Links, was dismissed by a judge in February last year.

Barnett's comments follow the case of Richard O'Dwyer, a 23-year-old British student who faces extradition to America for running another popular site, TVShack.net, which provided links to non-licensed streams of films and TV shows. O'Dwyer's family say they are baffled as to why American authorities want to try a British national with no US connection and whose site used servers based elsewhere.

Barnett, who heads ICE's efforts on intellectual property enforcement, said he could not comment on the O'Dwyer case. But in an interview with the Guardian he explained the broader thinking behind it.

"By definition, almost all copyright infringement and trademark violation is transnational. There's very little purely domestic intellectual property theft," he said.

The agency has been running a year-long campaign, Operation In Our Sites, which has thus far "seized" 125 of the most popular unlicensed film, TV and sport websites, including TVShack, as well as ones selling counterfeit physical goods.

Aside from the contravention of US trademarks, website names are central to deciding which are chosen, Barnett said: "The jurisdiction we have over these sites right now really is the use of the domain name registry system in the United States. That's the key."

The only necessary "nexus to the US" is a .com or .net web address for which Verisign acts as the official registry operator, he said.

Decisions on seeking extradition are down to the US department of justice. But Barnett said his agency – which has more than 7,000 criminal investigators – is actively pursuing those within its perceived jurisdiction: "Without wishing to get into the particulars of any case, the general goal of law enforcement is to arrest and prosecute individuals who are committing crimes. That is our goal, our mission. The idea is to try to prosecute."

In Our Sites has already prompted controversy elsewhere, with a Spanish company launching a lawsuit after two of its sports streaming sites were seized, even though they had been found not to contravene copyright law in Spain.

Barnett defended the decision to also go after linking sites: "I'll give you an analogy. A lot of drug dealing is done by proxy – you rarely give the money to the same person that you get the dope from. I think the question is, are any of these people less culpable?"

Civil rights and internet freedom organisations said they were alarmed at the apparent intention to enforce US copyright laws around the globe.

Isabella Sankey, director of policy for Liberty, said: "Many countries, including the US, are increasingly asserting jurisdiction over alleged actions that take place in other parts of the world. The internet increases our risk of falling foul of the law, making it possible to commit an offence on the other side of the world without even leaving your bedroom."

She called on the government to amend the UK's extradition agreement with the US so a British judge could decide where an alleged crime should be best tried. "It would allow UK courts to bar extradition in the interests of justice where conduct leading to an alleged offence has quite clearly taken place on British soil," she said.

Jim Killock, executive director of the Open Rights Group, which campaigns on web-based freedoms, said that domain names such as .com were usually regarded as generic.

"This seems absurd," he added. "If you don't have some idea that there's a single jurisdiction in which you can be prosecuted for copyright infringement that means you're potentially opening an individual to dozens of prosecutions."

Online piracy is, undoubtedly, a huge business. The 125 sites initially targeted for seizure by ICE – the majority of them selling counterfeited physical goods, almost all made in China – recorded between them around 60m visits even after they were replaced with a government warning notice. As well as TV shows and films, there is a huge trade in unlicensed video streams of sports events: just 10 of these sites received almost half the 60m hits.

While physical counterfeiting tends to be dominated by criminal gangs, Barnett said, entertainment sites are often run by the proverbial teenager in a bedroom – who can make a lot of money.

He said: "We seized one bank account for one individual running one sports streaming site. He lives with his parents and has no other source of income. He had $500,000 (£311,013) in his bank account. Most of the individuals that we've targeted were earning estimated amounts of between $10,000 and $20,000 a month. You've got to remember that the overheads are fairly low – your product isn't being paid for."