Kate Andrews, of the Institute for Economic Affairs, said the Labour Party leader’s approval of socialist regimes in countries including Venezuela and Cuba, showed he did not always put the interests of the UK first.
Speaking on Sky News, Smith attempted to defend Mr Corbyn but was shot down.
Ms Andrews, a news editor at the think tank, said: “He’s come out in support of things like Hamas.
“He has shown his sympathies there and he’s shown his sympathies for so many dictatorships across the world if they promote socialist values like in Venezuela and in Cuba.
Kate Andrews said Jeremy Corbyn had shown sympathies "for so many dictatorships"
You have to admit there is a kind of radicalism coming from his own personal views that have nothing to do with the benefit of the UK
“I think that the British public feels like, and I actually think Paxman did a pretty decent job last night pushing on this idea, yes it is absolutely fine that the Labour manifesto is not as radical as Jeremy Corbyn is, thank goodness.
“Coming out in support, whether it be through tweets or articles, even as recently as 2012/2013 about how great Venezuela is, as people die in the street.
“You have to admit there is a kind of radicalism coming from his own personal views that have nothing to do with the benefit of the UK, that we haven’t necessarily seen from any other politician.
“Forget the Tories, but Tim Farron and Ukip and the rest of it.”
Jeremy Corbyn in pictures Tue, July 12, 2016
Labour Leader Jeremy Corbyn takes part in a community meeting at the Guru Har Rai Gurdwara Sahib temple
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Britain's opposition Labour Party leader Jeremy Corbyn speaks at an anti-racism rally in London
Jones tried to fight back and said the British Government’s support of Saudi Arabia was much worse.
He added the Conservative Party was “rattled” over latest polls in the upcoming General Election, which takes place on June 8, and that explained with the Labour leader was being attacked.
“I think the British Government, look, they put the flag at half mast when the Saudi dictator died,” Jones said.
“We have explicit support for one of the most barbaric regimes on the face of the earth today.
“On the issues though, and I think this is the critical point, the Tories at the moment are rattled because they thought this would be a walkover.”
Both were quizzed by a studio audience on immigration, taxes and Northern Ireland.
Jeremy Corbyn once again denied links with the IRA which have dogged his campaign in recent days.
He refused to confirm or deny whether he would order a drone strike against overseas terrorists plotting a UK attack, and rejected claims that he would abolish the monarchy.
Labour is now just six points behind the Conservatives in the latest poll from ORB International for the Sunday Telegraph. Mr Corbyn's party were found to have 38 per cent of support, with the Conservatives on 44.