Downing Street has insisted there will be a firm end-date to the Brexit transition period, after a leaked document revealed the British government is challenging the EU’s 21-month limit and proposing that the UK stays in the single market and customs union as long as is necessary.

The government moved to avoid inflaming tensions with its pro-Brexit backbenchers, by dismissing the idea that a transition deal, which the government hopes to strike within the next few weeks, would be open-ended.

“There will be an end-date included in the agreement,” a Downing Street spokesman said. A cabinet minister told the Guardian any suggestion otherwise was “just paranoid or wishful thinking”.

The intervention came after a Whitehall position paper shared with EU member states on Wednesday appeared to leave open the possibility of an open-ended transition.

“The UK believes the period’s duration should be determined simply by how long it will take to prepare and implement the new processes and new systems that will underpin the future relationship,” the draft paper said.

“The UK agrees this points to a period of around two years, but wishes to discuss with the EU the assessment that supports its proposed end date”.

The EU had said that the transition period should end 21 months after Brexit day on 29 March 2019. During that period the UK will effectively remain a member of the single market and the customs union under the jurisdiction of the European court of justice, but without any say in the EU’s rules.

The EU’s chief negotiator, Michel Barnier, has claimed that 31 December 2020 is the most practical end date for the transition as it would dovetail with the end of the bloc’s seven-year budget and avoid the opening up of discussions on payments in addition to the UK’s £35-£39bn divorce settlement.

UK officials are insisting, however, that further talks are needed. They expect to finalise a non-extendable end date by the time of a meeting of EU leaders in Brussels at the end of March.

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Earlier this month, Barnier told MEPs in Strasbourg that he believed the UK did not want to formally request a longer transition period because it was too politically toxic for the prime minister to open up debate at home on how much more Britain would need to pay.

The government is under pressure to give UK businesses as much time as possible to prepare for Brexit. When the the prime minister suggested in her Florence house speech that the transition between Brexit and a the future trading relationship would last “about two years”, the CBI lobbied Downing Street to keep the door open to a longer period of adaptation.

The UK position document, leaked in Brussels ahead of it being formally presented to the House of Commons, nevertheless suggests that on the terms of the transition period the positions of the UK and the EU are broadly in line.

Beyond the end date, there remain substantive differences, however. The paper demands a right during the transition period for the UK to rewrite the fishing quotas that apply to its fleet under the common fisheries policy, a move that will face resistance in Brussels.

Rather than include a “punishment clause” in any agreement, through which the UK could be sanctioned for infringing the terms of the transition, the UK’s document says a joint committee should be established to ensure problems that arise are dealt with “in good faith” by both sides.

The UK is concerned about new laws that could do economic harm and wish to have a legal mechanism to resist such a scenario.

Downing Street also wants the right to opt in to future justice and home affairs policies and is questioning the EU’s insistence that sensitive information will not be shared with the UK as it is today.

The document does not make any demands over the rights of citizens who arrive during the transition period. However, speaking after prime minister’s questions on Wednesday, the prime minister’s spokesman reiterated that the government would not cave in to demands from the European commission, that EU citizens arriving during the transition period be granted the same rights as those already here.

“The people arriving after March 2019 arrive in different circumstances to people arriving before and can expect their rights to be different,” he said.