The prime minister said he wanted better trading and security relationships with Brussels as he vowed to rip up the "botched" deal struck by Boris Johnson.
Foreign Secretary David Lammy has already travelled to Europe for talks with key players, with a promise that the UK would be a "good neighbour" after the years of Brexit acrimony.
Speaking to reporters in Edinburgh, the prime minister said: "We intend to improve our relationship with the EU and that means closer trading ties with the EU, it means closer ties in relation to research and development and closer ties in relation to defence and security."
"I do think that we can get a much better deal than the botched deal that Boris Johnson saddled the UK with."
He added that it depends on "respectful relationships, talking to leaders across the EU and of course that work has already begun".
Lammy used his first trip abroad as the UK's top diplomat to make clear to his counterparts in Germany, Poland and Sweden about the chance to "seize the opportunity for a reset" and work "even more closely together to tackle shared challenges".
Lammy identified support for Ukraine and climate change, along with holidays and student exchanges, as areas where this can take place.
Elsewhere, Business Secretary Jonathan Reynolds said the return of freedom of movement with the EU was not on the table as part of efforts to improve post-Brexit trade.
Good to speak with — David Lammy (@DavidLammy) @JosepBorrellF on European security challenges, working together in support of Ukraine, and towards an immediate ceasefire in Gaza.As the world faces huge challenges, I look forward to strengthening UK-EU cooperation. https://t.co/0oVCE4xnc8July 7, 2024
Lammy spoke to EU foreign policy chief Josep Borrell and the pair agreed to meet "at the earliest convenience".
The Foreign Secretary could attend the September meeting of the EU foreign affairs council despite the UK no longer being a member of the bloc.
Borrell said the pair had a "good call" and discussed EU-UK cooperation in foreign and security policy, the latest developments in the Middle East and support for Ukraine.
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