Ken Clarke addressed young Conservatives at a London University
Mr Clarke and his fellow contender Iain Duncan Smith sought to move on from the in-fighting which followed Edgar Griffin's expulsion, by courting young Conservatives at meetings on Saturday.
"I do think Iain should make sure he is not attracting other people of this type and I just think the party quite rightly has got rid of him (Mr Griffin)."
Mr Clarke, speaking before an address to Young Conservatives at the University
of London said he could not guarantee that there would not be people with links to
the far right British National Party among his supporters.
But he added: "If I have got some member of the British National Party in my camp, the man must be an idiot if he doesn't realise what political stance I have got on the issue."
Mr Duncan Smith sacked Mr Griffin as a campaign aide when it emerged he had close links with the BNP, and the 79-year-old was later expelled from the Conservative Party.
His son is BNP chairman Nick Griffin and his wife Jean ran for the party against Mr Duncan Smith at the general election.
Outside his campaign headquarters in London, Mr Duncan Smith said his party now had to "rise above" the BNP controversy, and rejected claims that his camp had mishandled the situation.
He said: "I don't think it the BNP issue has done any damage at all, because we took swift action to deal with him Mr Griffin.
"I would say to all my colleagues and friends in the party, we really have to rise above this."
Mr Duncan Smith, who was also meeting Young Conservatives on Saturday, accused the Labour Party of trying to stoke the row.
He said: "They want the Conservative Party to have a go at each other in this leadership election, and I am simply not going to oblige them.
"At the end of this, I want to unite the Conservative Party and, if Ken wins, exactly the same."
'Vilification campaign'
But the Shadow Defence Secretary has accused his opponent of a campaign of "vilification and smears".
Asked whether the exchange of words on Saturday showed that the Conservative Party was as split as ever, Mr Clarke replied: "It shows that one or two people in his camp have slightly lost their head, lost their cool.
"I totally agree with Iain that we have no truck with those sort of people."
Student backing
Mr Clarke's views have managed to attract the support of some young Conservatives.
Several Tory student leaders came out in support of Mr Clarke for the leadership of the party on Saturday, saying he is the man to reclaim the centre-ground of British politics.
In a letter to The Independent newspaper on Saturday, they urged members to reject what they call the "outdated right-wing" agenda of Mr Duncan Smith.
The three authors were Nigel Fletcher, vice-president, University of London Union; Mark Aspinall, West Midlands area convenor, National Union of Students; and Richard Hilton, vice-president of King's College London Students' Union.