Ministers have agreed any "backstop" arrangement to prevent the return of a hard border between Northern Ireland and the Republic after Brexit should not continue for more than a year after the end of the transition period.
A British government technical note said the UK expected permanent customs arrangements to be in place by the end of December 2021 at the latest.
The move came after Brexit Secretary David Davis was reported to be considering resigning unless there was a clear time limit on the temporary customs arrangements which would be adopted if there is no final Brexit deal.
The note said: "The UK is clear that the temporary customs arrangement, should it be needed, should be time limited, and that it will be only in place until the future customs arrangement can be introduced.
"The UK is clear that the future customs arrangement needs to deliver on the commitments made in relation to Northern Ireland.
"The UK expects the future arrangement to be in place by the end of December 2021 at the latest. There are a range of options for how a time limit could be delivered, which the UK will propose and discuss with the EU."
Downing Street said earlier that Mrs May had held "constructive" talks with Mr Davis and expected him to remain in his post.
The British prime minister also held separate face-to-face discussions in her parliamentary office with the two other leading Brexiteers, Foreign Secretary Boris Johnson and International Trade Secretary Liam Fox.
None of the three ministers threatened to resign during the discussions, a spokeswoman for the prime minister said.
A source close to Mr Davis said: "Obviously, there's been a back and forth on this paper, as there always is whenever the government publishes anything.
"The backstop paper has been amended and now expresses, in much more detail, the time-limited nature of our proposal - something the prime inister and David Davis have always been committed to."
Under the current timetable Britain is due to leave the EU on March 29 2019 followed by a transition period running to the end of 2020.
The paper proposes that if there is no final agreement, there should be a temporary customs arrangement lasting up to 12 months.
During that period there would be no "tariffs, quotas, rules of origin (or) customs processes" applied to UK-EU trade.
At the same time the UK would be able to strike free trade agreements with other countries and to implement those elements which did not affect the functioning of the backstop.
The paper was issued after Mr Davis was believed to have insisted the UK should be able to unilaterally withdraw from any border agreement to maintain leverage with Brussels in negotiations.
Pressed on whether he could remain in post if the backstop deal did not meet his full approval, Mr Davis said on Wednesday: "That's a question, I think, for the prime minister, to be honest."
Mr Davis made it clear the document would be "decisive" as he said he planned to meet chief EU negotiator Michel Barnier again for Brexit talks next week.
I welcome publication of #UK proposal on customs aspects of IE/NI backstop.
— Michel Barnier (@MichelBarnier) June 7, 2018
We will examine it with 3 questions: is it a workable solution to avoid a hard border? Does it respect the integrity of the SM/CU? Is it an all-weather backstop?
