The rival claims by Zanu-PFC and the Movement for Democratic Change (MDC) reflect a bitter rivalry that was exacerbated by deadly violence in the capital.
Six people were killed when police and army fired live rounds to disperse a protest on Wednesday by opposition supporters in Harare. In addition 14 were injured and 18 people were arrested at the offices of the MDC, police said.
The Zimbabwe Electoral Commission said it will start announcing results of the presidential election at 10pm local time (8pm GMT) on Thursday, though by law it has five days from the vote on Monday to deliver the final tally and it has sometimes given conflicting statements about when it is releasing information.
International election observers urged the commission to reveal the presidential results as soon as possible, saying delays will increase speculation about vote-rigging.
Meanwhile, a spokesman said the main opposition candidate, Nelson Chamisa, was being investigated by police for allegedly inciting violence.
Mr Chamisa, opposition politician Tendai Biti and several others are suspected of the crimes of “possession of dangerous weapons” and “public violence,” according to a copy of a search warrant, which was seen by The Associated Press.
The warrant authorises police to search for and confiscate any evidence as part of their investigation.
President Emmerson Mnangagwa and the ruling Zanu-PF party have accused the opposition of inciting the deadly violence. The opposition, human rights activists and international election observers condemned the “excessive” force used to crush the protests and appealed to all sides to exercise restraint.
Opposition demonstrations had broken out after electoral officials said the ruling party had won a parliamentary majority in the elections, and Paul Mangwana, a Zanu-PF spokesman, said at a news conference he anticipated similar success in the presidential race.
Elsewhere in Harare, Mr Chamisa said he was confident that his MDC party would be forming the next government. As the rival camps sparred over the election outcome, they also appealed for calm amid a fog of conflicting accounts. Mr Mnangagwa said his government was in touch with Mr Chamisa in an attempt to ease the tensions, though the opposition leader said he had not received any communication.
Soldiers cleared people from the streets of central Harare on Thursday after they swept in and opened fire on Wednesday to disperse protesters who alleged vote-rigging in the peaceful election, the first without long-time leader Robert Mugabe on the ballot. The electoral commission has said the vote was free and fair.
A credible vote is crucial to the lifting of international sanctions imposed on Zimbabwe so that its collapsed economy can recover. Elections under Mr Mugabe’s 37-year rule were marked by violence and intimidation against the opposition, as well as numerous allegations of fraud.
Mr Mnangagwa, who is close to the military, called for an “independent investigation” into the violence in Harare, saying those responsible “should be identified and brought to justice”.
The military deployment was the first time that soldiers had appeared in the streets of the capital since Mr Mugabe’s resignation in November after a military takeover. At that time, thousands of jubilant residents welcomed the soldiers as liberators.
Some Harare residents, standing amid the shattered windows of the violence, expressed frustration and exhaustion.
“We are a peaceful nation,” said 29-year-old Sifas Gavanga. “We don’t deserve the death we saw.”