"I've seen a number of prime ministers in operation over the years - I go right back to Margret Thatcher - I think she's very good, she makes good decisions, she's bold, she takes her time".
Reports are swirling of Conservative MPs promoting both Mr Davis and Philip Hammond as potential Prime Ministers in a bid to keep Boris Johnson out of Number 10.
Another cabinet minister, International Development Secretary Priti Patel, also refused to rule out taking part in a leadership contest.
The Brexit Secretary has been tipped to take over from beleaguered Theresa May if she is ousted from office.
He said: "Yes. I take my share of the blame for it, along with the other twenty members of the Cabinet who all said it was a good idea".
He said: 'There is no essay crisis about this government. Point number two is I want a stable backdrop to this Brexit negotiation, it's hard work by the way'.
China, US kick off inaugural diplomatic, security dialogue
China will be represented by senior foreign policy adviser Yang Jiechi and the chief of staff of the military, Fang Fenghui.
Addressing Tory rebels directly, he said: "Don't be so self-indulgent".
'Stop being so self indulgent and get on with the day job which is that people put us here to deliver - to deliver a decent economy deliver a decent life for them and to deliver Brexit, and we'll deliver all those things.
He went on: "Don't be so self indulgent, is my message to those [plotters].the more you do of that, the more self indulgent nonsense you go in for, the more hard you make it to do our proper job".
Davis, who launched the Brexit talks with European Union negotiator Michel Barnier last week, also threw his support behind Prime Minister Theresa May, saying he took his share of the blame for advising her to hold an early election this month in which her Conservatives lost their parliamentary majority.
He admitted that he had urged Mrs May to call the disastrous snap election which ended in her losing her majority entirely.
Interviewer Andrew Marr pointed out that Mr Davis had made a particular point of pushing for the election and asked if he had apologised to Ms May for the advice, to which the minister responded after a hesitation: "I didn't apologise to her".
Asked if Mrs May would have to quit before the next General Election, she said: "I disagree - because the reality is we are living in quite unprecedented times".
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