But the Movement for Democratic Change (MDC) wants to put it to a referendum.
Political observers have interpreted this as a sign that Zanu-PF will spurn the mediation efforts led by the Southern African Development Community and South African President Jacob Zuma. Earlier this year, Mugabe said his party reserved the right to reject Zuma as the SADC facilitator if he showed "any bias".
Zuma's team, led by his international relations adviser Lindiwe Zulu, arrived in Harare last week in an effort to break the protracted deadlock over the draft constitution, which also threatens to affect the timing of the referendum, which has been scheduled for October.
Tendai Biti, the MDC's secretary general and a negotiator involved in trying to break the political impasse, said the bickering over the draft constitution could see the country sliding back into chaos.
"The people of Zimbabwe have suffered and if Zanu-PF persists on its current stance, I foresee months and months of attrition and debilitating negative energy, which will throw this country backwards."
Under the terms of the global political agreement signed in September 2008 between Mugabe, MDC leader Morgan Tsvangirai and Arthur Mutambara, leader of a smaller MDC faction, a referendum cannot be held until all political parties have endorsed the draft constitution. Using this loophole, Zanu-PF has produced its own draft constitution. It said its version countered the committee's document that "ignored the people's views" and it wants a referendum on it.
But Zanu-PF would prefer to stick to the current Lancaster House agreement, drawn up in 1980 and amended 19 times to favour Mugabe.
War of the drafts
Political analyst Trevor Maisiri from the International Crisis Group said: "There is no way that we can take two drafts through, because that will basically culminate in a war of the drafts. This can be a recipe for serious political clashes and violence.
"At the same time we cannot discard the stakeholders' conference and parliamentary process that are meant to follow, because these are the legal steps highlighted in the global political agreement.
"Taking two drafts to the referendum will mean having to amend the agreement and that, to some extent, remains a serious challenge," Maisiri said.
Political insiders who spoke to the Mail & Guardian this week confirmed that the MDC's top brass were seriously considering Zanu-PF's demands to have its draft also tested in a referendum.
Tsvangirai last month hinted at the possibility at a press conference and Biti, ranked second-highest in the MDC, said this week that the suggestion might be accepted.
"The parties came up with their own draft on July 18, but Zanu-PF wants to exercise veto power over the people of Zimbabwe. So let us take their [Zanu-PF] draft, let us have two drafts, and the people of Zimbabwe will either reject both drafts or vote for the draft that they think is closer to what they aspire for. Let the people of Zimbabwe decide."
Among the contentious issues are dual citizenship, the death penalty, devolution of power, abolition of the office of the attorney general – to be replaced by a national prosecuting authority – and the requirement that presidential candidates must have running mates in the next election.
Zanu-PF spokesperson Rugare Gumbo said his party condemned in the "strongest terms" attempts by the MDC to give a false impression that the "revolutionary" party's proposed amendments to the draft constitution were tantamount to producing a new document.
"Zanu-PF only made eight crucial amendments based on issues to do with the country's national liberation struggle, indigenisation and, above all, our independence and sovereignty", Gumbo said.