Rivals for the Conservative leadership have said there must be no uncontested “coronation” for leadership frontrunner Boris Johnson.
Several candidates said the party needed to learn from the experience of electing Theresa May unopposed in 2016.
“Let’s not make the same mistake again,” said Home Secretary Sajid Javid.
It comes as Mr Johnson expressed fears about damaging “blue-on-blue” attacks in forthcoming TV debates.
While he has agreed to take part in the BBC’s debate on Tuesday, Mr Johnson will not be taking part in Sunday’s debate on Channel 4, with his team reportedly having reservations about its proposed format.
Mr Johnson was criticised for avoiding scrutiny and taking a “presidential” approach to the contest to be the next Tory leader and prime minister by International Development Secretary, and fellow contender, Rory Stewart.
“The whole genius of British politics is that we don’t behave like American presidents, sweeping up in a motorcade. We’re all about talking to people,” Mr Stewart said.
Mr Stewart said that Conservative members “deserved to have a choice” in the final ballot and “coronations are not the way to do democratic politics”.
His comments were echoed by Mr Javid, as he arrived at a London meeting for leadership candidates to speak to party members.
“We had a coronation the last time. That didn’t work out well, so let’s not make the same mistake again,” said Mr Javid.
‘Nerve and mettle’
Senior Conservative Party figures were reportedly drawing up plans for other candidates to withdraw from the contest after Mr Johnson gained 114 votes in the first ballot – more than double his nearest rival, Mr Hunt.
The Daily Telegraph said that the Tory whips’ office drew up the plan to avoid weeks of internal party conflict.
It would mean Mr Johnson would be the only candidate to go forward to the final postal ballot of party members, making his election a formality.
Foreign Secretary Jeremy Hunt told the BBC that most people wished “there had been more scrutiny” in 2016. He pledged to emulate David Cameron in the 2005 leadership contest, who came from behind to earn a victory that “shocked everyone”.
Mr Johnson avoided reporters as he arrived at the meeting – a hustings organised by the National Conservative Convention, where he and other leadership candidates will address potential voters.
Earlier, former Brexit secretary Dominic Raab said the next party leader needed to be thoroughly tested in the heat of debate.
“Everyone is going to have to demonstrate that they have not just the vision, but the nerve and mettle to deal with the EU and with a minority government,” he told The Daily Telegraph.
“If you can’t take the heat of the TV studios, what chance of taking the heat of the negotiating chamber in Brussels?”
He also contrasted his own background as the grammar school-educated son of a refugee with the “privileged elite”, and said he would be more likely to unite working class and middle class voters.