The Conservatives currently command a majority of four in parliament's lower House of Commons
Boris Johnson challenged his rival for Britain's leadership on Tuesday to deliver Brexit by the end of October whatever happens, only to be accused once again of trying to avoid scrutiny.
Johnson, the former foreign secretary and ex-mayor of London, is the favourite to succeed Theresa May as leader of the governing Conservatives and therefore as prime minister.
But his rival Jeremy Hunt, the current foreign secretary, has accused him of being a "coward" for refusing to face him in a one-to-one TV debate.
The pair are battling for the votes of an estimated 160,000 Conservative party members, with the winner declared on July 23, and taking office on July 24.
Johnson has sold himself as the charismatic leader to guide Britain through troubled times, despite questions over his competence and populist rhetoric.
But after weeks spent avoiding media interviews, he has been accused of ducking scrutiny.
He has been called upon to explain exactly how he would leave the European Union, and why police were called to a noisy row with his girlfriend last week.
Johnson broke cover in a series of broadcast interviews on Monday night and Tuesday, when he refused to discuss his private life but gave further details on his Brexit strategy.
He followed up with a letter to Hunt, challenging him to commit to keeping to the latest delayed Brexit date of October 31, "deal or no deal".
"We must not kick the can down the road again," he wrote in the message posted on Twitter.
Johnson was a leading campaigner for Brexit in the 2016 EU referendum, whereas Hunt backed staying in the bloc -- a disadvantage among the largely eurosceptic Conservative membership.
But Hunt hit back at Johnson's letter by asking again why his rival refused to attend a Sky News TV debate that had been planned for Tuesday evening.
"Hi Boris, it's good to talk. But no need for snail-mail, why not turn up to Sky tonight and I'll give you full and frank answers? #BoJoNoShow," he tweeted.
'Do or die'
Critics of Johnson question his position on Brexit, asking how he can maintain the support he has secured among die-hard eurosceptic Conservative MPs and moderates alike.
In an interview with TalkRadio, he said he would keep the October 31 date "do or die, come what may".
However, he acknowledged that he would need the cooperation of Brussels to cushion any economic disruption from the divorce, telling LBC radio: "There has to be agreement on both sides."
The Conservatives currently command a majority of four in parliament's lower House of Commons.
Around a dozen Conservative MPs are also said to be ready to bring down a Johnson government in order to stop a "no deal" scenario.
Both Hunt and Johnson are hoping to renegotiate the divorce deal May struck with the EU, which parliament has repeatedly rejected -- even though Brussels says this is not possible.
Johnson said on Tuesday he wants to keep "the best bits", protecting the rights of EU expats and setting up a post-Brexit transition period while removing its arrangements for the Irish border.
If that fails, he suggested a "standstill" trade deal under World Trade Organization rules, although this needs EU agreement.
He said Britain would threaten "no deal" and withhold its £39 billion ($50 billion) share of EU liabilities until this is done.
However, the EU has repeatedly said it will not sign any deal that does not include the "backstop" plan to keep open the border between the UK's Northern Ireland and EU member the Republic of Ireland.
The backstop would keep Britain in the EU's customs union and require Northern Ireland to follow other rules set by the bloc until another way was found to avoid border checks.
Johnson said "technical fixes" could provide an alternative way of verifying the origin and compliance of goods without physical frontier checks, but admitted there was "no single magic bullet".