* Rivals ask: Why is Johnson avoiding scrutiny?
* New PM won't change EU exit deal - Commission
* Daily Mail: Come out of your bunker, Boris
* Johnson due to open campaign on Wednesday (Adds comment from candidate Rory Stewart)
By Guy Faulconbridge and Kylie MacLellan
LONDON, June 11 (Reuters) - Boris Johnson, the favourite to succeed British Prime Minister Theresa May, was criticised on Tuesday by rivals who said the former foreign minister was avoiding public scrutiny in the contest.
After three years of political deadlock over Brexit, the ruling Conservative Party is picking a new leader from 10 candidates and hopes to have a new prime minister in place by the end of July.
Johnson, who led the official campaign to leave the EU in the 2016 referendum, is the frontrunner to replace May despite a long record of scandals and gaffes. Betting markets give him a 60 percent probability of winning the top job.
But rivals have turned on Johnson over his pledges to cut taxes for the wealthy, deliver Brexit with or without an exit deal and his apparent desire to keep a low profile.
Rival Matt Hancock said: "I certainly think that everybody who puts their name forward to be prime minister should be open to scrutiny, should be accountable.
"Everybody should participate in the proposed TV debates. And I think we've got to ask the question: why not?" he told BBC radio. "I've got nothing to hide and that's why I am here."
When asked about Johnson, Mark Harper, another candidate, said: "If you've got nothing to hide, you won't mind answering questions."
Candidate Andrea Leadsom, said: "The country needs to get their chance to really look at, in detail, the candidates that are up in front of them and Boris will definitely get that scrutiny."
A spokesman for Johnson did not respond to requests for comment. Johnson left his home in London on Tuesday without comment, a Reuters reporter said. He is due to begin his campaign on Wednesday.
The United Kingdom could be heading towards a constitutional crisis over Brexit as many of the candidates vying to succeed May are prepared to leave the EU on Oct. 31 without a deal but parliament has indicated it will try to thwart such a scenario.
May resigned after repeatedly failing to get parliamentary support for the exit deal she had negotiated with Brussels.
European Commission President Jean-Claude Juncker on Tuesday reiterated the EU's refusal to renegotiate the withdrawal deal.
A European Commission spokesman, asked about a pledge from Johnson to withhold billions in liabilities owed to the EU's budget, said: "Everybody knows what is on the table. What is on the table has been approved by all member states and the election of a new prime minister will not change the parameters."
One candidate for the leadership, Rory Stewart, questioned Johnson's suitability to be prime minister.
“Is this the person that you want writing the instructions to the nuclear submarines?," he said on Tuesday.
“Is this the man that you want embodying your nation on the world stage and guiding you through the most difficult choice that Britain has faced for 50 years?"
Rivals say Johnson, a former London mayor, is avoiding the limelight because the contest is his to lose - a stray word or poorly placed joke could deprive him of his chance at getting Britain's top job.
Johnson made his name as a European Union-bashing journalist in Brussels, then entered politics in the Conservative Party. He also raised his profile through a series of appearances on a television comedy.
He upset some Europeans before Britain's Brexit referendum by comparing the goals of the EU with those of Adolf Hitler and Napoleon.
His eccentric style helped him shrug off a series of scandals, among them getting fired from the party’s policy team while in opposition for lying about an extra-marital affair. Tabloid newspapers dubbed him "Bonking Boris" for those episodes.
This might have sunk others, but Johnson became increasingly popular, culminating in his two victories in usually left-leaning London’s mayoral contests in 2008 and 2012.
He was considered a favourite for the top job when David Cameron resigned after the 2016 referendum. But his ally, Michael Gove, deserted him and announced his own candidacy.
Gove, again one of his main rivals for the leadership, on Monday taunted Johnson, saying, "If I get through, which I am sure I will, actually, to the final two against Mr Johnson, this is what I will say to him: 'Mr Johnson, whatever you do, don’t pull out'".
Reporting by Guy Faulconbridge Editing by Michael Holden, Janet Lawrence and Frances Kerry