The Department for Exiting the European Union said there could be "a temporary customs union between the UK and the EU" to help businesses make the transition to life outside the EU.
Brexit Secretary David Davis said the transition period could last about two years.
In the long term, the department said, a "customs partnership" could eliminate the need for a border for goods travelling between Britain and the EU. Alternately, it suggested "a highly streamlined customs arrangement" could be set up, using technology to ease border procedures.
"To be in & out of the Customs Union & 'invisible borders' is a fantasy," tweeted Guy Verhofstadt, the European Parliament's Brexit coordinator.
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Some British businesses have accused the government of being vague about whether there will be economic barriers with the EU after Brexit in March 2019. The persistent uncertainty - 14 months after Britain voted to leave the EU - is weighing on the economy.
Trade Secretary Liam Fox and Treasury chief Philip Hammond wrote in the Sunday Telegraph that in 2019 Britain will leave both the EU's single market in goods and services and its customs union.
The British proposal says the UK should be free to negotiate new trade relationships during the transition period, something EU officials are likely to find problematic.
Scottish First Minister Nicola Sturgeon, who favours Britain's staying in the single market and customs union, accused the government on Twitter of having a "daft 'have cake and eat it' approach."
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