Davis said he could not support May's plan to maintain close trade and regulatory ties with the European Union, which he said gave "too much away, too easily".
Conservative leading body the 1922 Committee had a meeting to decide the Prime Minister's fate following the resignations. "I believe that is what people voted for when they voted to leave and we will deliver in faith with the British people", she said.
"The general direction of policy will leave us in at best a weak negotiating position and possibly an inescapable one", he said in his letter. Trump isn't expected to directly address Brexit, nor were he and Johnson scheduled to meet.
We have postponed crucial decisions - including the preparations for no deal, as I argued in my letter to you of last November - with the result that we appear to be heading for a semi-Brexit, with large parts of the economy still locked in the European Union system, but with no United Kingdom control over that system.
His exit raises questions about the position of Prime Minister Theresa May, with further departures following months of infighting within her leadership circle possible.
In her response, Mrs May said that "I do not agree with your characterisation of the policy we agreed at cabinet on Friday".
Juncker had a phone call with May on Sunday evening before Davis resigned, but officials gave no details on the conversation.
Davis's late-night resignation undermines May's fragile government.
"It seems to me we're giving too much away, too easily, and that's a unsafe strategy at this time", Davis said in a BBC radio interview Monday morning.
Hunt, 51, had served as health minister for more than 5-1/2 years, the longest term of any in the history of the state-funded National Health Service, weathering doctors' strikes, public discontent with funding levels and other challenges.
Prime Minister Theresa May has defended her Brexit plans.
Johnson and Davis are two of the most prominent proponents of a so-called "hard Brexit", or a clean break with the EU.
Mrs May however appears to have lived to fight another day, with no vote of no confidence tabled by her MPs.
Yet he and Johnson have shared a mutual affinity for one another, so his departure may put the already tenuous U.S. -U.K. relationship on even shakier ground, especially if May enters into conversations with Trump from a weakened position.
So at the previous Chequers session we thrashed out an elaborate procedure for divergence from European Union rules.