Writing in the Brexit-backing Telegraph, the ministers said there would be a "transition period" if the United Kingdom leaves the 28-country block as expected in March, 2019, to avoid an economic "cliff edge" which many businesses and economists fear.
But in a joint article for The Sunday Telegraph newspaper, they agreed there should not be a "cliff-edge" when Britain leaves in March 2019.
"Once the interim period is over, we want a permanent, treaty-based arrangement between the United Kingdom and the EU which supports the closest possible relationship with the European Union, retaining close ties of security, trade and commerce", they said.
"I've launched this process because with time of the essence, we need to get on with negotiating the bigger issues around our future partnership to ensure we get a deal that delivers a strong United Kingdom and a strong EU", David Davis, the secretary of state for exiting the European Union, said in a statement.
They said any transition period would be "time-limited" and that Brexit would mean Britain pulling out of both the European single market and the customs union.
Such an arrangement was criticised by eurosceptics as a betrayal of the swift Brexit they wanted, and has even raised concerns the process would be stopped altogether after Britons voted in a referendum in June 2016 to leave the bloc.
Prime Minister Theresa May then called a snap election in an attempt to increase her Conservative Party's majority in Parliament and strengthen her negotiating hand.
The UK Department for Exiting the European Union said Sunday it hoped to persuade the 27 other EU nations to start negotiating a "deep and special" future relationship to include a free trade deal between Britain and the EU.
Brexit Minister David Davis (L) and EU Chief Negotiator in charge of Brexit negotiations Michel Barnier seen at a press conference at the EU Commission Headquarters in Brussels, on July 20, 2017.
The British government is fighting back against criticism that it is divided and unprepared for Brexit, announcing it will publish a set of detailed proposals on customs arrangements, the status of the Ireland-Northern Ireland border and other issues.
Mr Barnier has maintained that negotiators must make progress on the rights of European Union and British citizens, the border with Ireland and Britain's exit payment before discussing a trade deal, while the prime minister Theresa May wants an accord before leaving.
A second batch of papers, to be released in the run-up to the October meeting of the European Council in Brussels, will look at "future partnership" arrangements between the United Kingdom and the EU, including the UK's proposals for a new customs arrangement with the bloc.
The government will this week publish the first of three discussion papers ahead of the next round of negotiations, scheduled to start August 28 in Brussels, Brexit secretary David Davis's office said on Sunday.