Mandelson's comments to reporters came as Cameron, leading the campaign to stay in the European Union in a June 23 referendum, faced attacks from within his own Conservative party.
Those supporting Brexit moved ahead in a leading average of opinion polls Monday, just over two weeks before the vote.
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"That's why you're seeing the agitation, the daily headlines delivered courtesy of the pro-Brexit press on behalf of the 'Leave' campaign," he added.
"That's how they want him to be seen because they think in that way they will reduce support for him."
Leading Conservatives including former London mayor Boris Johnson and justice minister Michael Gove are campaigning to leave the EU.
Mandelson was a European commissioner from 2004 to 2008 and a leading figure in the Labour governments of Tony Blair and Gordon Brown.
He is a member of Britain's House of Lords and wants the country to remain part of the EU.
"People correctly perceive the risks but they do not yet fully understand why the danger of leaving the EU and its single market is so great for the economy," he added. "That's our job to explain".
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