In a preliminary assessment released a day after the vote, the Zimbabwe Election Support Network said that the count at polling stations was going smoothly. But it reported that some voters had been turned away at 6 percent of polling stations nationwide, and at 19 percent in Harare, an opposition stronghold.
There were also “incidents of intimidation, harassment or violence” in a limited number of polling stations, according to the network, a private Zimbabwean organization that deployed 6,500 observers across the country.
Andrew Makoni, the network’s chairman, said it was too soon to say whether the problems resulted from logistical issues or from fraud.
“We are in the process of collating all those reports to really be in a position to assess the nature of the irregularities,” he said.
The voting was free of the widespread rigging and violence that marred previous elections under Mr. Mugabe, who was ousted in November after more than 37 years in power. But the main opposition party immediately questioned the validity of the poll and, if the race for president proves very close, those doubts are sure to intensify.
In the race for the presidency, both the governing party candidate, President Emmerson Mnangagwa, and his main rival, Nelson Chamisa, expressed confidence in victory on Tuesday, though no vote tallies had been made public. Election officials said that results of the contest would be announced by Saturday, or within five days of the vote, as required by law; if no one wins over 50 percent of the vote, a runoff will be held in early September.
The presidential race had been considered too close to call. Mr. Mnangagwa, 75, the incumbent who seized power from Mr. Mugabe and is the candidate of the ruling ZANU-PF party, is hoping that a win in a free and fair election would bring him personal legitimacy and economic assistance for Zimbabwe from the West.
For decades, Mr. Mnangagwa acted as Mr. Mugabe’s enforcer and played a leading role in rigging past elections. But as president, he has differentiated himself from his predecessor by reaching out to Western officials and investors, especially the British, as well as to white Zimbabweans.
The main opposition candidate, Mr. Chamisa, 40, outmaneuvered older and more experienced rivals to win the leadership of the Movement for Democratic Change Alliance after the death this year of its longtime leader, Morgan Tsvangirai, who ran twice against Mr. Mugabe. A skilled orator, Mr. Chamisa, who is also a pastor, energized supporters at scores of rallies across Zimbabwe in recent months.
Mr. Chamisa has made statements casting doubt on the integrity of the electoral process. A couple of days before the vote, he said that a victory by Mr. Mnangagwa would be “fiction” — despite the fact that a poll by Afrobarometer, a nonpartisan research organization, had shown him slightly behind Mr. Mnangagwa.
In a tweet on Monday, Mr. Chamisa accused election officials of causing delays to suppress the vote in the opposition’s urban strongholds. “The people’s will being negated and undermined due to these deliberate and unnecessary delays,” he wrote, though he offered no evidence.
At a news conference on Tuesday, Priscilla Chigumba, the chairwoman of the Zimbabwe Electoral Commission, denied that officials had deliberately caused delays. Despite Mr. Chamisa’s tweet, she also said that the commission had not received any complaints of fraud from any candidate.
Election officials were poised to announce results in some local races by Tuesday evening.
Observers from the European Union and the United States were expected to release their assessments of the elections on Wednesday.
On Monday, international observers said that the voting appeared to have proceeded peacefully nationwide. But they also said that there had been reports from many polling stations where voters had failed to cast a ballot — some because their names had not been registered and others because the process was taking hours.
The refusal of election officials to post voter rolls at the entrance of polling stations, as requested by the opposition and observers, appeared to have exacerbated those problems.