"That included building on the close defence and security ties already forged between the UK and European Allies to drive greater cooperation across all areas of the relationship," Burnham said.
UK Prime Minister Andy Burnham has said Britain must be "bolder" in seeking to rebuild relations with the European Union, according to his office.
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Burnham made the comments during a meeting with European Council President António Costa on board a train to Kyiv on Sunday evening. The pair travelled to the Ukrainian capital to mark Ukraine's Independence Day on Monday.
"The UK had to be bolder in terms of getting closer to the bloc," Burnham told Costa during the journey, a Downing Street spokeswoman said.
"That included building on the close defence and security ties already forged between the UK and European Allies to drive greater cooperation across all areas of the relationship," he added.
The spokeswoman said the pair also agreed that the UK-EU summit scheduled for later this year "would offer a platform to continue that work."
The UK has been on a mission to repair its relations with the EU over the last two years as the country looks to leave the divisiveness of the 2016 Brexit referendum behind.
Former Prime Minister Keir Starmer, who pledged to put Britain "at the heart of Europe," began the push to forge renewed ties with the bloc, agreeing a Brexit "reset" with Brussels in 2025 that he said would slash "red tape and bureaucracy."
Despite this, differences remain on both sides and progress has been slow, with a proposed youth mobility scheme proving particularly sticky.
Talks had been due to continue on the reset in July, but a planned summit was postponed following Starmer's resignation.
Burnham, who took office in July, has previously called for the UK to rejoin the EU, but he distanced himself from those comments while campaigning for the Makerfield by-election earlier this year.
The former mayor of Greater Manchester said that while he still believed the Brexit vote had hurt the UK, he did not think it was the right time to readdress the issue.
"My view is that Brexit has been damaging," Burnham said in May. "But I also believe the last thing we should do right now is re-run those arguments."
Ukraine
Burnham is making his first international visit as prime minister this week as he meets Ukrainian President Volodymyr Zelenskyy in Kyiv.
In a speech delivered from the city on Monday, Burnham reiterated his support for Ukraine in its fight against Russia and Vladimir Putin's invading forces.
"We are with you in this struggle all the way heart and soul," he said. "And as prime minister, let me say that I am with you personally," he added.
Since Moscow launched its full-scale invasion of Ukraine in February 2022, the UK has provided a range of military and economic support to Kyiv and has committed £25 billion in funding.