A dozen Conservatives have now declared their intention to fight for the top job after Theresa May resigns as Tory leader on 7 June.
Mr Harper, the MP for Forest of Dean, has not served in Mrs May’s government – a distinction he said sets him apart from his rivals.
“We’ve seen basically the same faces saying the same things that they’ve been saying for the last three years,” he told the Daily Telegraph.
“A number of them have tried to position themselves as fresh faces but I’m afraid they’ve sat around the Cabinet table sharing the responsibility with the prime minister.
“I am quite happy to acknowledge that in this contest I am the underdog.”
Mr Harper, who campaigned for Remain in 2016, suggested a further delay to Brexit beyond 31 October could be needed if the next prime minister wanted to renegotiate the Brexit deal – something some of his rivals have already ruled out.
Meanwhile, all the candidates in the Tory race have been warned of the dangers of a no-deal Brexit by the Confederation of British Industry (CBI).
The organisation’s director-general Carolyn Fairbairn used an open letter to say the next prime minister must seek an agreement with Brussels as the “vast majority of firms can never be prepared for no-deal”.
One of Mr Harper’s Tory leadership rivals, Esther McVey has said the UK needs to “actively embrace leaving the EU without a deal”.
Frontrunners Boris Johnson and Dominic Raab have both said they would work to renegotiate the terms on offer with Brussels but would make sure the UK leaves on 31 October, with or without an agreement.
In her open letter to the participants in the race for Number 10, the CBI’s Ms Fairbairn said: “The next prime minister can only claim the Conservatives are the party of business if they secure a Brexit deal that protects the economy, jobs and living standards.
“Firms large and small are clear that leaving the EU with a deal is the best way forward.
“Short-term disruption and long-term damage to British competitiveness will be severe if we leave without one.
“The vast majority of firms can never be prepared for no-deal, particularly our SME (small and medium enterprise) members who cannot afford complex and costly contingency plans.
“We need compromise, consensus and honesty to resolve the Brexit impasse, quickly.”
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