Owen Smith, a former member of Corbyn's top team, accused the veteran socialist yesterday of "sloganising" rather than holding the Conservatives to account, and of failing to campaign hard enough to prevent a vote to leave the European Union.
Corbyn hit back by accusing Smith and other Labour MPs who have rebelled against him in recent months of undermining their efforts to win the next election, telling his rival: "You walked away."
The 67-year-old refused, noting he was elected only last September on the back of strong grassroots and trade union support -- prompting his critics to back the relatively unknown Smith as an alternative.
Corbyn has the support of many Labour members, and since February 2015 party membership has surged from 200,000 to 540,000.
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"People see in Corbyn a new form of politics, where people care for the poor and downtrodden," said Philip John Rosser, a 61-year-old former lecturer attending the hustings in Cardiff in Wales.
In the debate, 46-year-old Smith repeatedly cited the latest opinion poll putting the Conservatives 14 points ahead, and another that found 29 percent of Labour voters would prefer May to Corbyn as premier.
For some party members, his message is getting through.
"I'd rather see Jeremy Corbyn but there's no point having him if he's not going to win," said Chris Jones, a 28-year-old civil engineer.
The battle for control of the party has exposed long-standing fault lines over Labour's core values, and led to fears that it could split, with Smith warning this week that it was "teetering on the brink of a precipice".