"There can be no monkeying around" with the transition period, Johnson said.
While the former journalist is now ineligible to stand in any Tory leadership contest (party rules say candidates must be serving MPs) she is often touted as a future leader of the party.
Boris Johnson has said any post-withdrawal transition period must not last "a second more" than two years, while some senior Conservatives have said Britain should walk away from Brexit negotiations by Christmas if no serious progress is being made.
"What I have is a cabinet that is united in the mission of the government", she said.
Despite the hurdles in becoming leader, bookmakers still reckon Ms Davidson is a worthy outside bet, with her current odds of 16/1 putting her ahead of Cabinet big hitters like Michael Gove and Damian Green.
The event was held in the State Department's Maps Room, which is supposed to be used only as government property and as official duties of ministers, the newspaper said.
State Department Will Not Recognize Kurdish Independence
Millions of Iraqi Kurds were called to a referendum Monday to decide whether to break away from Baghdad or to remain part of Iraq. They come a day after Iraq instituted a flight ban that halted all worldwide flights from servicing the territory's airports.
"If you run any organization... and something goes monumentally wrong, as did the election. then the buck does have to stop with that individual", Grant Shapps - former Conservative Party chairman - said.
Michael Gove and the International Trade Secretary Liam Fox were also present to endorse the new institute, which Mr. Fox said showed the moral imperative to lower trade barriers."We may think the benefits of free trade are self-evident but we need to sell benefits to the public", said Mr. Fox.
Another ex-frontbencher said: "Some Brexiteers would have been happy [with his interventions] but at the end of it they want our party to deliver Brexit".
Asked whether Mr Johnson should be sacked, the Chancellor told ITV's Good Morning Britain: "We all serve at the Prime Minister's pleasure and we all owe the Prime Minister our allegiance and our loyalty within the Cabinet".
He told Radio 5 Live's Pienaar's Politics: "It is extremely sensible when you are in government to express [your] views in private rather than public". It's advice for all my colleagues at all times.
On Mr Johnson's interventions, Mr Gauke said: "I think it is for Boris to determine how much he wants to say".
The Prime Minister's Florence speech opened up a war of bids for her attention from Brexiteers and Brexitsceptics alike, all of whom believed that the Prime Minister is so malleable on policy that she just needs to hear the same thing over and over again before she believes it.