Ursula von der Leyen, the nominee to lead the European commission, has signalled she will not reopen Brexit talks with the next British prime minister and stressed the “precious” Irish backstop must be defended.

She said she still hoped the UK would remain in the European Union, while indicating she had no intention to renegotiate the withdrawal deal agreed by Theresa May and EU leaders.

“I think it’s a good deal, but it is your responsibility and your noble task to sort this out,” she told a British Liberal Democrat MEP in the European parliament, in her first public comments on Brexit.

In a thinly veiled message to the Tory leadership candidates Jeremy Hunt and Boris Johnson, Von der Leyen said the tone and attitude with which Brexit happens were crucial, adding: “Brexit is not the end of something, Brexit is the beginning of future relations and it’s of absolute importance that we have good cooperation.”

She also made it clear she opposed attempts by both men to reopen discussions on the backstop, the fallback plan to avoid a hard border on the island of Ireland.

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“I think the backstop is of utmost importance and we absolutely know how crucial this nonexistent border is for you,” she said in response to an Irish MEP. “Having the backstop in the Brexit deal is precious, important and has to be defended.”

Von der Leyen was addressing the European parliament’s liberal group as part of a round of meetings with large political groups to rally support ahead of a vote on her appointment next week. After being backed by EU leaders Von der Leyen needs at least 376 MEPs to elect her as commission president.

The current German defence minister is a member of the centre-right European People’s party (EPP), so needs to win over some combination of socialists, liberals, greens or Eurosceptics.

Von der Leyen, who would be the first woman to lead the EU executive, said she wanted an equal share of men and women as European commissioners. However, this depends on the EU’s member states appointing women to be their commissioners – an appeal many ignored in 2014.

Brexit is scheduled for 31 October, the day before the new European commission takes office.

Making her pitch to MEPs, Von der Leyen emphasised her green credentials while also arguing that the EU needed to be more assertive in the world – a traditional preoccupation of the centrist group. Her earlier meetings with the EPP, Eurosceptic group and socialists were not broadcast online.

She pledged her full commitment to making the bloc climate neutral by 2050, saying this required tougher targets for 2030 as well as EU funds for countries that would otherwise struggle to make the green transition.

Poland, the Czech Republic and Hungary recently blocked an EU declaration for a net-zero carbon emissions target by 2050, and are angling for more money before signing up to any pledge.

Speaking in a mix of English, French and German, Von der Leyen emphasised her European outlook, reminding MEPs she was born in Brussels and attended the city’s European school with Dutch, German and French classmates. “That was my first impression of Europe,” she said.

She clarified her views on European defence, restating that national parliaments should continue to have the final say on sending men and women into dangerous situations. “I prefer to speak about the army of the Europeans, not the European army,” she said, citing as a model the existing cooperation between Dutch and German forces.

Although it is expected Von der Leyen will be approved by the European parliament, she still faced sniping over the process of her appointment whereby she leapfrogged politicians who had declared bids to lead the commission before European elections.

The Dutch MEP Sophie in ‘t Veld asked whether she would be tougher in acting against violations of the rule of law and democracy than the outgoing commission, adding it was “remarkable” that Poland and Hungary had supported Von der Leyen’s nomination.

Von der Leyen answered “yes” and pointed out her appointment was backed by all countries, although Angela Merkel, the German chancellor, did not vote for her because of divisions in Germany’s ruling coalition.

In her opening remarks Von der Leyen said the rule of law was “the jewel in the crown of our work” and that the EU needed a mechanism for upholding it in member states.