"Unless we show fortitude and determination, I don't think we will carry conviction in Brussels about the deal we want to do".
Mr Johnson said the "fundamental flaw" in the current Withdrawal Agreement is the Irish backstop, and claimed a solution could be found.
Mr Johnson was the clear victor in the first ballot with 114 votes - 71 votes ahead of his nearest rival, Jeremy Hunt.
"We can have that debate only if our front runner in this campaign is a little bit braver in terms of getting out into the media, engaging in debates, engaging in the TV debate", Mr Hunt told BBC Radio.
Meanwhile, there was anger at a reported plan for the other contenders to pull out next week with only Mr Johnson's name going forward to the final ballot of grassroots members in July.More news: Patriots file tampering charges against Texans amid pursuit of Nick Caserio
"When you campaign in marginal seats, who can reach out and unite the working-class vote and the middle-class vote?"
The leadership contest in the UK's ruling Conservative Party follows May's decision to resign last month after she was unable to deliver Brexit.
British politician Boris Johnson took a big step toward succeeding Theresa May as prime minister, winning the first round of Conservative Party voting Thursday. "I will now look for the best way to advance the values we fought for".
The victor will become new party leader and automatically replace May as premier, most likely at the end of July.
Health Minister Matt Hancock quit the battle to succeed Mrs May as Conservative Party leader, saying the party was looking for a candidate for the present not the future, leaving six contenders, among whom Mr Johnson is the overwhelming favourite.More news: Hong Kong protests planned as groups slam police
The favourite to be the next United Kingdom prime minister, Boris Johnson, has been ordered to defend himself in court after a district judge ruled that he should answer for his infamous, and oft-disputed, claim that the United Kingdom sends £350 million a week to the EU.
He tweeted: "I have chose to withdraw from the race to be the next leader of the Conservative Party".
Johnson vowed Wednesday that as prime minister he would "get Brexit done", either by renegotiating May's rejected Brexit deal or by leaving the European Union on October 31 without an agreement.
Mr Johnson received more than double the number of votes of his nearest rival - Foreign Secretary Jeremy Hunt - putting him well on course to secure one of those two spots. He resigned previous year over May's handling of Brexit and later described May's strategy as putting a suicide vest on Britain and handing the detonator to European officials.
"The test is, is this person sufficiently moral to be prime minister, and I believe he fails that test". The two will then face the second phase of the election, in which over 1.2 lakh members of the party will vote.More news: Armenia's politicians donate blood on World Blood Donor Day
Told that was a shocking comparison, Mr Amin said: "Yes".