The Government had a responsibility to ensure performers were properly rewarded for their work, he said on a visit to the Brit Performing Arts and Technology School in Croydon, south London.
Persistent file-sharers could have their internet connections cut off for short periods, he said, but only after a series of written warnings.
Singer Lily Allen recently issued a rallying call to fellow artists to back tough action, warning that illegal file sharing was making it “harder and harder for new acts to emerge”.
Lord Mandelson said: “People in the industry are right to be concerned about how we nurture and protect talent in the future.
“We cannot see a situation where people are recording and producing content in Britain only to see it ripped off unlawfully without proper payment.
“Equally we have got to look to the industry to put in place services, packages and products that are affordable, that give people access to the music they want to hear.”
The cut-off sanctions, which are out for consultation until September 29, have been criticised by internet service providers who said they could amount to a breach of internet users’ human rights.
Lord Mandelson said such sanctions were under consideration, but would only be used in extreme circumstances.
“We are talking about temporary suspension of persistent unlawful file sharers after many written notifications with the chance for them to appeal,” he said.
“It doesn’t get more modest or more fair than that.”
The Business Secretary said it was vital for jobs and growth that Britain’s creative industries were given the chance to flourish.
“Downloading somebody’s work without paying for it - whether it be music, film or computer games - is not a victimless act,” he said.
“It poses a genuine threat to our creative industries and to the livelihoods of talented, hard-working people striving to get a foothold in them.”
Internet connection suspension is among the options being considered by the Government as it prepares to legislate following the Digital Britain report, which was published in June.
The Government hopes to include anti-piracy measures in the Digital Economy Bill, which is due before Parliament in November.
Accompanying Lord Mandelson on the visit today were Culture Secretary Ben Bradshaw and singer Leona Lewis, who is a former pupil of the Brit School.
They watched a young band rehearsing for a gig, a performance which had the two ministers clapping and tapping their feet to the music.
Lewis said: “I had a great time at the Brit School.
“It encouraged my creative talent and gave me an understanding of the music business as well as getting an education at the same time.
“I learned how the performance industries actually work and how much work goes on behind the scenes into creating, recording and releasing a song.
“It’s important that people understand how copyright means that performers and writers can actually end up making a living out of their work.”
Lord Mandelson said the industry had a responsibility to offer customers good alternatives to illegal downloads and welcomed commercial services like Spotify.
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