Andy Burnham has said he will back sweeping changes to the electoral system to make politics “less point-scoring, more problem-solving” if he becomes prime minister.

The Greater Manchester mayor has previously called for the introduction of proportional representation for UK general elections, handing more power to minority parties like the Greens.

In an interview with BBC Radio Manchester on Thursday, Burnham gave his clearest commitment yet to electoral reform if he wins the Makerfield byelection – to be held on 18 June – and then a leadership contest to No 10.

He said he believed in “a different type of politics – a politics that is more place first rather than party first”, adding: “Where you can work with others, you do that. I do think there needs to be reform to the electoral system to enable less point-scoring, more problem-solving – that’s what I think we need. Less short term, more long term.”

Burnham did not say when he would like to see these changes introduced or whether he would commit to starting the process if he becomes prime minster this year.

Keir Starmer, who faces a potential ousting by Burnham, told reporters on Thursday he planned to campaign for the mayor. “Yes, and I’ve said to the whole Labour movement that I want everybody to be involved in the campaign, whatever other discussions are going on, it’s really important – that’s a straight fight between Labour and Reform,” Starmer said of the byelection.

On Thursday one of the mayor’s keen supporters in parliament, Luke Charters, resigned as a frontbench aide, saying he had taken the decision in order to speak out and urge the party to be bolder.

Charters, the MP for York Outer, was one of the first MPs to head to Makerfield last Friday to begin the campaign for Burnham hours after the byelection was announced.

“As a party, we have to be bolder with our ideas and more confident in our approach, kinder to ourselves as one Labour family, and we must make people in every corner of this country feel that politics is genuinely working for them in their everyday lives,” he said, resigning from his post as a parliamentary private secretary in the Department for Business and Trade.

One of the parties that would benefit most from electoral reform would be the Greens, which has reportedly considered dialling down its Makerfield campaign if Burnham’s team commit to introducing proportional representation.

But the party’s campaign was in disarray on Thursday when, hours after announcing its candidate, Chris Kennedy, the party said he had dropped out “for personal and family reasons”.

Critics of proportional representation have said it would lead to a more chaotic form of government, with unstable coalitions and an inability to pass legislation. Yet Burnham has long argued that Britain has suffered from an overcentralised, London-centric form of government where two parties dominate at the expense of many of the UK’s nations and regions.

Burnham also used his BBC Radio Manchester interview to distance himself from claims that he would seek to immediately rejoin the EU.

Standing by his previous comments that he would like the UK to rejoin the European bloc “in my lifetime”, he said: “The country has to fix itself and we have to get to the heart of some of these fundamentals that don’t work for people and that has got to be our relentless priority in the next five or 10 years before we then worry about our relationship with other places.”

Burnham is facing a tough challenge from Nigel Farage’s Reform UK to win one of the most consequential and highest-stakes byelections in recent decades.

The former Leigh MP, who was first elected to parliament 25 years ago and ran twice unsuccessfully for Labour leadership, said his nine years as Greater Manchester mayor had framed his vision for changing the UK.

“I really believe that politics in this country is at a moment where we either change it or it really becomes quite broken and people lose faith completely and that’s a dangerous place for the country to get,” he told BBC Radio Manchester.

“I think part of the problem is … the whole system down there [in Westminster has] … not been run for our part of the world. Politics is made for other people in other places and not been wired for these parts of the world – and that’s what I’m in this to change. If politics doesn’t change in this country I don’t know where we will end up in a few years time.”

He described his leadership bid as an attempt to “change Labour” and return it to “the party people perhaps once knew when they were younger, solidly on the side of working-class people and working-class communities”.