Earlier this week a court ruled that Labour could not bar new members from taking part in the leadership selection, with Smith immediately responding with a call for an extended contest.
And now the Labour challenger's team have formally laid out their demands, writing to party general secretary Iain McNicol to request an additional two weeks to reflect the need for the newly enfranchised members to choose a candidate.
In a letter to McNicol, Smith's campaign chair Kate Green said the verdict poses challenges to the party's ability to verify and check memberships, especially Labour's plan to appeal the verdict.
"It is a distinct possibility that ballot papers will be issued on 22 August just days after the right to vote is confirmed to a large element of the membership," Green said.
"We fear that giving some members as little as a week between confirming their vote and ballot papers landing is not sufficient time for them to gather the information they will wish to have about the candidates before they cast their vote."
It comes after Smith last night admitted the court ruling "probably" favoured Corbyn's bid to remain at the helm of the party.
Speaking on ITV News last night, Smith said of the newly enfranchised Labour members: "I don’t know what the split is going to be. I think it’s probably going to be in Jeremy’s favour. It’s very clear that I’m the underdog in this."
A two week delay would means that Labour would not actually appoint a leader until 8 October, more than three months after a Labour MPs launched open rebellion against Jeremy Corbyn's leadership in the aftermath of the Brexit vote.
It also means that the party will not choose a new leader in time for its annual conference, currently set to take place in Liverpool between 25 September and 28 September.
The process contrasts markedly with the Conservative Party's rapid selection of Theresa May as its new leader - aided by the early withdrawals of Boris Johnson, Stephen Crabb and Andrea Leadsom - which took place just over two weeks after David Cameron resigned.