He then took a shot at Johnson's apparent lack of media appearances during the leadership race, without calling him out outright.
Would Boris Johnson make a good Prime Minister?
Each candidate must be nominated by at least eight Conservative MPs.
Lorraine Kelly, a mainstay of British morning television who combines a sunny outlook with plain-speaking Scottish patter, delivered an unusually pointed series of barbs over two days, directed at one of the outsiders in the 10-strong field to succeed Theresa May as leader of the governing Conservative Party.
"Without Brexit, there will be no Conservative government and maybe no Conservative party", foreign minister Jeremy Hunt said at his campaign launch.
But "whether he can actually achieve that is another matter", the expert said.
She ran against May for Tory leader in 2016, quitting the race after receiving harsh criticism for saying motherhood helped make her qualified to lead; May has no children.
Charismatic and popular among grassroots Conservatives, he is less liked by Conservative MPs sceptical of his bombastic style and chequered track record.
It's just another measure of how odd a contest is under way to be Prime Minister that a politician likely to make the divisions besetting Britain even worse than they already are is seen as the best option by those who might give him the job.
Her aim is for a "managed exit" keeping the least controversial bits of May's deal with Brussels, she said, conceding that if the European Union rejects her approach, Britain would leave the bloc without agreement.
Johnson initially attempted to become prime minister in 2016 shortly after the Brexit referendum, but his campaign imploded soon after and May was anointed without a party-wide leadership contest.
It isn't the first clash between the candidates, with Michael Gove hitting out at Boris Johnson during his campaign launch yesterday.
The date of 25 June would ensure this process is in place before the end of the Tory leadership contest, and before MPs leave for parliament's summer recess.
These two will then be chosen in a postal ballot by more than 160,000 paying party members. Regarded as even-tempered and competent, he managed to navigate a heated contract dispute with doctors in the National Health Service when he was health secretary, securing a deal after a long-standing argument.
"We won't deliver Brexit with bluff and bluster", added another leadership candidate Dominic Raab, 45, a former Brexit secretary who has also taken a tough line on Brexit but insisted on Monday that he doesn't want to leave without an agreement.
Among some of the others who formally launched their leadership bids on Monday include United Kingdom health secretary Matt Hancock, who called for a "fresh start", and former Brexit Secretary Dominic Raab, who unveiled proposals to redirect GBP 500 million a year from the UK's aid budget to create an worldwide wildlife fund to save endangered species and habitats.