The Opposition leader would change his political views if he fully grasped the German theorist's works, Lord Reid claimed.
Corbyn has spoken out on previous occasions, most recently during the Labour leadership contest, saying he believed “we all owe something to” the man who laid the intellectual foundations of Communism, adding Marx “analysed what was happening in a quite brilliant way”.
He acknowledged then, though, that he had “not read as much of Marx as I should have done”.
But speaking on Thursday, Lord Reid, a peer who held numerous top-level Cabinet posts between 2003 and 2007, said Marx’s philosophy vindicated New Labour’s approach to politics.
“I’m not sure he’s done the elementary work on Marx’s own thought because, if he did, he would take a different view of the world.
"Because we’re now in an era where the most important productive forces are cyber, where the social and economic changes have meant that working people under capitalism are a thousand times better off than they were 100 years ago.
"Therefore we have to change the way we apply our values – which was what New Labour was about – in order to win that electorate.”
After discussing his own transition from being a Labour-backer to a Communist supporter, then returning to the Labour fold again, Lord Reid said Corbyn had to understand that the policy prescriptions to put in place socialist principles were different today than they were in the past.
“The retention of values, the concern about the impoverishment of people, the disadvantaged, the concern for justice and so on – I think the retention of those is something I would say is a strength,” he said.
“However, if you think you can apply that, despite all the changes of history, the way they were applied 50 years ago or 100 years ago, it’s a weakness because – especially in a democracy – you have to compromise with an electorate, an electorate which is... changing...
“So retain your values by all means... but the way in which you apply them in different circumstances has to differ as the world changes.”
The comments come after two embarrassing incidents for the Labour Party over their ties to the far-left.
Shadow chancellor John McDonnell first proceeded to quote from Chairman Mao's 'Little Red Book' and gift a copy to George Osborne.
Weeks later, Corbyn reportedly quoted from ruthless Albanian dictator Enver Hoxha at a Labour Christmas party.
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