Nick Clegg has called Lord Sugar "thin-skinned" after the businessman unleashed a volley of abuse at him on Twitter.
The Apprentice star hit out after the Deputy PM suggested millionaires like him should not receive pensioners' perks such as free bus passes and winter fuel payments.
In a string of messages attacking "Calamity Clegg", the Labour peer called for Prime Minister David Cameron to "silence" his deputy for making the coalition "look like a joke".
He wrote: "Calamity Clegg, as he should be known, is talking rubbish. I don't have bus pass and I pay for my TV licence like everyone else.
"Clegg is an embarrassment to coalition for his gaffes. I don't have and don't want a free bus pass. I pay for my TV Licence as I am 66 not 75.
"Why doesn't Cameron silence this idiot Clegg? How many more gaffes can he spout off on TV? Makes the coalition look like a joke."
Mr Clegg laughed when he was asked during his weekly LBC radio show how he felt about the tycoon's onslaught.
"He's slightly thin-skinned," he said. "He drives around in this great big Bentley on primetime television, he wafts around the House of Lords in ermine, and then he seems to be very offended when I point out that he has got a bob or two.
"I don't see why someone like him should be entitled to a winter fuel payment.
"No doubt, having said that, I will get another torrent of classic Sugar tweet-abuse this morning. Anyway, that's the way I see things."
Mr Cameron has vowed to keep pensioner benefits in place until 2015, but Mr Clegg said earlier this year that the idea of universal benefits had to be looked at again.
Shadow chancellor Ed Balls has also said Labour would scrap winter fuel payments for wealthy pensioners.
The handouts are worth £200 to the over-60s and £300 for those over 80 - with differing amounts for couples and people living in care homes.
Under Labour's plans, the richest pensioners who have enough income to pay higher or top-rate income tax - around 600,000 people at present - would lose the money.