David Davis said he did not accept claims that he was known as a "thug" and a "bully" by political colleagues, in an interview on BBC Newsnight.
David Davis said the Tories could win under his rival David Cameron
Interviewer Jeremy Paxman said Mr Davis had also been dubbed "an adventurer, disloyal, congenitally treacherous".
Mr Davis dismissed the quotes as "the gossip of politics" from one or two people, saying he disputed all of them.
However, he conceded: "In politics sometimes if you really want to get things done you make enemies."
During the half-hour interview, Mr Davis was questioned about his claim he would cut taxes by £38bn a year by the end of his parliament if he became prime minister.
Asked if this was a promise, he said: "This is the strategy ... there will be a reduction in taxes to create growth in the economy."
Pushed further on whether he was guaranteeing to reduce taxes by this amount, he said: "I did not use the word guarantee, I said it was a strategy."
He was also asked about the government's Terror Bill and whether he believed it was right that chief police officers had become involved in contacting MPs ahead of the Commons vote.
"The position of the chief constables looks a little political, but frankly I have not made an issue of it because frankly the substantive issue is centred somewhere else ... but I do worry about it," said Mr Davis.
He spoke of his desire to withdraw the UK from the 1951 Convention on Refugees and creating new ways to balance the number of immigrants coming in, with the skill shortages.
On the European Union, Mr Davis was clear that his policy did not involve withdrawal, but said he was investigating the Human Rights Act and whether it could be replaced, repealed or reformed, possibly with a "bill of rights".
Mr Davis's rival in the Conservative leadership contest David Cameron will face questioning from Jeremy Paxman next Thursday 17 November.
The full Jeremy Paxman Interview with David Davis can be viewed on Newsnight's website.