The public should be able to vote for the next Labour leader, with contenders taking part in a series of debates, Health Secretary Patricia Hewitt says.
Patricia Hewitt has been the MP for Leicester West since 1997
She has urged her party to "seize this opportunity" to reach people who would not normally take part in the process.
The move would restore the electorate's confidence after recent "infighting", which had been "politics at its worst", she wrote in the New Statesman.
Prime Minister Tony Blair has promised to stand down as leader within a year.
At present, up to one million people are likely to have a say in picking his successor, but all of them will already have some kind of tie to Labour.
The decision lies with an electoral college split equally three ways between the 354 Labour MPs, all party members and anyone belonging to affiliated trade unions.
"Imagine a leadership contest that brought together not just members but people who used to support us or might do so in future, to discuss our country's response to climate change or social cohesion," Ms Hewitt wrote.
"At hustings across the country, candidates would discuss these issues with people from all sides of the debate, as well as with each other, in person and on the web.
"Such an approach would not only help ensure Labour remains in touch with people's concerns but also raise public understanding of the difficult decisions all governments face."
The Leicester West MP said a "new politics of public engagement" would "enormously strengthen the authority of the new leadership".
The overwhelming favourite to take over as leader is Chancellor Gordon Brown, but left-wing backbencher John McDonnell has also said that he will stand as a candidate.
Education Secretary Alan Johnson has already confirmed he wants to be considered for deputy leader, but has declined to say if he will seek to be leader.
Northern Ireland Secretary Peter Hain has announced his intention to stand as deputy when John Prescott steps down, and Constitutional Affairs Minister Harriet Harman has said she is considering whether to do the same.