France has reiterated its opposition to Britain being granted any further Brexit extension if it does not have a concrete plan with clear support in the House of Commons, saying that without that Britain must be deemed to have chosen to leave the EU without a deal.

Theresa May wrote to the president of the European council, Donald Tusk, on Friday to ask for Brexit to be delayed until 30 June while she battles to win cross-party agreement on a way forward.

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Responding to May’s letter, France’s secretary of state for European affairs, Amélie de Montchalin, told the Guardian in a statement: “The European council took a clear decision on 21 March … Another extension requires the UK to put forward a plan with clear and credible political backing.”

The council would then have to define the necessary conditions attached to that extension, she said. “In the absence of such a plan, we would have to acknowledge that the UK chose to leave the EU in a disorderly manner.”

Tusk is pushing the EU27 to offer a one-year “flexible” extension to article 50, with an option to leave earlier once the withdrawal agreement is ratified by parliament. He is said to have described the plan as “the only reasonable way out”.

De Montchalin said Paris had “read with interest Theresa May’s letter to President Tusk. As the prime minister rightly wrote, the current impasse is not in the best interest of either the UK nor the EU. It cannot be allowed to continue.”

In the letter to Tusk, sent after a second day of talks with Labour, May said both parties accepted the need to pass the legally binding withdrawal agreement but had not reached consensus on the future relationship.

If that was not possible, May said, she hoped to agree with Labour a process for parliament to choose between possible options, the outcome of which both sides would promise to accept.

That could allow parliament to ratify the deal, pass the necessary legislation and leave before 22 May, meaning the UK would avoid participating in European parliament elections, the prime minister added.

But she conceded that the government would be legally obliged to hold those elections if it had not left in time.

Asked why May was seeking a date that had already been rejected, her spokesman said there were “different circumstances now” to when she requested the 30 June date before the last European summit, and that the prime minister had pledged to not seek an extension beyond that date.