The Mail on Sunday claimed that in the leaked memo, Britain Foreign Secretary Boris Johnson and Environment Secretary Michael Gove demanded that transition arrangements for Britain's exit from the EU should wrap up on June 30, 2021.
The newspaper quoted a senior source in the UK government as saying that Johnson and Gove had carried out a "soft coup"; the source also referred to PM May as "their Downing Street hostage."
Citing May's "sensible pragmatism", the letter said that it "does not in any way dilute our ambition to be a fully independent self-governing country by the time of the next election."
"If we are to counter those who wish to frustrate that end, there are ways of underlining your resolve," according to the letter.
Titled EU Exit — Next Steps, the memo is marked "For your and Gavin's eyes only," in an apparent nod to May's chief of staff Gavin Barwell.
The letter emerged shortly after the Sunday Times reported that at least 40 Tory MPs had secretly agreed to ink a letter of no confidence in May as the Brexit talks are thought to be coming to a standstill.
"Continuing uncertainty about the government’s approach to Brexit is now the biggest risk facing our country. The prime minister must end the confusion, take on the 'no-deal' extremists in her government and back a jobs-first Brexit for Britain… It is time for Theresa May to stop dithering and decide: whether to govern or go," Labour Party leader Jeremy Corbyn wrote in an op-ed for The Sunday Times newspaper.
The Brexit negotiations between London and Brussels, which kicked off on June 19, are expected to wrap up by the end of March 2019.
In a referendum on June 23, 2016, about 51.9 percent of British voters said "yes" to their country leaving the EU.