And, in a clear attempt to emulate the Labour Party which elects its leaders through an electoral college of MPs, unions and members, he announced that if he wins the leadership ballot he would give his party the chance to endorse or reject the decision at a special party conference, and would abide by its decision.
But Iain Duncan-Smith, a supporter of John Redwood, dismissed Mr Hague's call for party endorsemet as "a gimmick."
The former Secretary of State for Wales, at 36 the youngest of the six contenders by nine years, said he was "flattered" to be picked out by Mr Dorrell as the only one worthy of a head-to-head, but suggested that he felt such a meeting unnecessary.
The move followed an earlier rejection by Mr Hague of an attempt by Michael Howard, the former home secretary, to include him in his own campaign as running-mate.
At a press conference yesterday, the 45-year-old former health secretary claimed Mr Hague was the only other candidate who represented a clear break with the past for the party. He had written to him to suggest a debate under a neutral chairman, he said.
"This debate will allow both of us to set out our approach to the task which lies ahead, and it will allow the party to make an informed choice between us," he said, adding that both he and Mr Hague offered the party a choice to take on a leader from "the next generation".
In the first formal news conference of his campaign, Mr Dorrell also spoke of his desire to "democratise" the party and ensure all its supporters were engaged in its processes. He suggested that under a new constitution, which would follow a review of the whole party organisation, there should be an annual leadership re-election campaign.
Two hours later, Mr Hague issued a statement claiming such a meeting was unnecessary as he was meeting more than 1,000 members of his party in a series of six regional meetings .
He also had "an extensive programme of private meetings with colleagues to address any issue they wish to. I believe this approach is the most constructive way of addressing the issues and concerns of Parliamentary colleagues and the wider Conservative Party rather than the divisive format of a debate," he said.
Mr Hague began the day by opening the day's Parliamentary debate on the Queen's Speech for the Opposition, and ended it with the first of those meetings in his home territory of South Yorkshire. In the next fortnight, he will also speak in Edinburgh, London, Bristol, Coventry and Manchester.
He told the Commons the Government's devolution plans would be "the most far-reaching constitutional changes for years," and warned against gagging backbenchers who objected.
A MORI poll for yesterday's Times showed Mr Hague battling with Mr Redwood for second place behind Kenneth Clarke, with both the party faithful and the public.Reuse content