"I have no expectation of mass suspensions. People will receive two notifications and if it reaches the point [of cutting them off] they will have the opportunity to appeal," Lord Mandelson told the audience at the C&binet Forum, a talking shop set up by government to debate the issues facing the creative industries.
The pay-off for tough penalties against persistent file-sharers would be a more relaxed copyright regime, Lord Mandelson said.
The details of it would need to be hammered out at European level but it would take account of the use of copyright material "at home and between friends", he said.
It would mean that, for example, someone who has bought a CD would be able to copy it to their iPod or share it with family members without acting unlawfully.
Lord Mandelson praised the UK's creative industries, which are worth around £16bn and employs 2 million people.
But it has been eroded in recent years, he said, by new ways of accessing content.
"I was shocked to learn that only one in 20 music tracks in the UK is downloaded legally. We cannot sit back and do nothing," said Lord Mandelson.
The fact that young people now expect to download content for free was "morally as well as economically unsustainable," he added.
But he emphasised that "legislation and enforcement can only ever be part of the solution".
The long-term answer was for the industry to educate users and to offer new and cheaper ways to download content, he said. In addition, new copyright laws were needed to lift restrictions on how people moved content on to the various different devices that they owned.
In France the government has just approved a so-called three strikes policy.
Under its system, those identified as illegally downloading content would initially be sent warning letters and, if they failed to comply, could be removed from the network for up to a year.
UK internet service providers have argued that it is not their job to police the network, claiming that there are "mere conduits" of content.
They also say that they should not have to bear the brunt of the costs.
In his speech, Lord Mandelson said that the costs of enforcing the policy would be "shared between ISPs and content providers".
The Internet Service Providers' Association thinks rightsholders should shoulder the burden for all costs, including the reimbursement of ISPs.
"This approach is consistent with the principle of beneficiary pays and would serve to incentivise rightsholders to develop new business models and ensure an effective and efficient use of notifications and targeted legal action," read a statement from ISPA.
ISP TalkTalk said that it would "continue to resist any attempts to make it impose technical measures on its customers".
It has set up a campaign called Don't Disconnect Us to lobby against the plans.
it said that it believed the "three-strikes" rule would lead to "wrongful accusations".
"The unintended consequence of Lord Mandelson's plan will be to encourage more wi-fi and PC hi-jacking and expose more innocent people to being penalised."
The firm recently demonstrated how someone could hi-jack unsecured wi-fi connections to download music illegally.
The Open Rights Group, a digital rights lobby organisation, has long been opposed to a disconnection policy.
Jim Killock, executive director of the Open Rights Group, is disappointed that the UK government is determined to introduce such legislation.
TalkTalk security expert Matt Roxburgh demonstrates the problem to Rory Cellan-Jones
"Even MI5 disagree with Mr Mandelson - they are convinced we will see a rise of a 'Dark Net' of infringers. Nobody at C&binet from an online music service, as opposed to an old media company, thought that peer-to-peer [file-sharing] was a threat to their businesses.
"Yet Mandelson seems determined to push forward with his plans for 'three strikes' - threatening to punish people extremely harshly, threatening their education, businesses and livelihoods for a relatively minor financial misdemeanour," he said.
There has been increasing pressure from the music industry to get tough on pirates.
Lily Allen has been spearheading a campaign against music piracy, with high-profile stars including Gary Barlow and James Blunt behind her.
Lily Allen has spearheaded a campaign against music piracy
Music industry group BPI welcomed the move.
"The measures confirmed today by government are a proportionate way of encouraging illegal file-sharers to embrace the new services, and will drive further innovation that will benefit online consumers," said Geoff Taylor, BPI chief executive.
But not all content providers agree. Fast-growing music streaming service we7 thinks the government has missed the point.
"Piracy is a reaction to an unsustainable situation, where reasonable, legitimate access to music has struggled to match demand," said chief executive Steve Purdham.
"A variety of reasonable and sustainable models for providing music to consumers is key to ending rampant piracy. This is the approach that should be taken by the government rather than criminalising consumers and driving pirates further into the undergrowth," he added.
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