It says political tensions following last month's presidential election make it impossible to hold a free and fair run-off in the near future.
The electoral commission has still not issued the results of the poll.
But says the ruling Zanu-PF party has won the first of 23 seats to complete a recount, according to the Herald.
The opposition says its candidate, Morgan Tsvangarai, won March's presidential vote outright.
But the electoral commission says it cannot publish the official results until it completes a recount of presidential and parliamentary votes in a number of disputed constituencies.
The Herald said the electoral commission had confirmed Zanu-PF's victory in Goromonzi West, one of only two constituencies where the opposition Movement for Democratic Change (MDC) had requested a recount.
According to the commission, Zanu-PF actually picked up just one extra vote and confirmed it as the winning party.
Policy shift?
The opinion piece in The Herald says other Southern African countries should act as mediators between the government and opposition, to form a unity government which could organise new elections and write a new constitution.
Zimbabwe's President Robert Mugabe has been under fire over March's disputed elections. His neighbours have been supportive but regional differences are now emerging.
It also says the West must lift economic sanctions.
The unity government would be headed by Mr Mugabe.
It may be too soon to suggest that the article represents a significant shift in party policy, says the BBC's Peter Greste in Johannesburg, but it may well reflect a strand of thought within Zanu-PF.
Mr Tsvangarai's MDC accuses supporters of the ruling Zanu-PF of voter intimidation and beatings ahead of an expected second round.
Post-election violence in Zimbabwe has displaced 3,000 people, injured 500 and left 10 dead, according to MDC secretary general Tendai Biti.
Justice Minister Patrick Chinamasa denied anyone had died in political violence.
The leader of the governing ANC in South Africa, Jacob Zuma, is refusing to blame Mr Mugabe for the violence.
Speaking to the BBC during a visit to London, Mr Zuma said the violence in Zimbabwe was unacceptable, but he wasn't prepared to judge individuals.
He also refused to criticise President Thabo Mbeki's "softly softly" approach as mediator.
"We are doing something more than anybody else in reality... other people are doing absolutely nothing."

Source: BBC