Zimbabwe's opposition says its candidate, Nelson Chamisa, has won Monday's presidential election.
The MDC Alliance said the ruling Zanu-PF party was attempting to rig the vote to allow President Emmerson Mnangagwa to win, and the delay in releasing official results was unacceptable.
The electoral commission urged patience, saying it needed time to collate the votes.
The polls were the first since long-serving ruler Robert Mugabe was ousted.
The vote attracted a high turnout of 70% and was monitored by international observers.
Speaking at a press conference in the capital, Harare, the MDC Alliance's Tendai Biti said there was a clear attempt by Zanu-PF to interfere "with the people's will".
He warned the party not to "plunge Zimbabwe into chaos".
The opposition announcement pre-empted official results.
A Zanu-PF spokesman told the BBC he had "no clue" what Mr Biti was talking about.
And Home Affairs Minister Obert Mpofu said those who violated election rules by prematurely declaring victory risked incurring the "wrath of the law".
Zanu-PF, which has been in power since Zimbabwe gained its independence in 1980, has been accused of rigging previous elections to keep Mr Mugabe in office.
Mr Mnangagwa has promised a free and fair election.
What's been the reaction on the streets?
There have been celebratory scenes outside the MDC Alliance headquarters in Harare.
Crowds have been blocking the road, singing and dancing, since Mr Biti said that Mr Chamisa had won.
A truckload of policemen and water cannon drove near the building in an apparent show of force.
However, many businesses reopened on Tuesday after being shut on voting day, a public holiday.
When will we know the official winner?
The Zimbabwe Electoral Commission (Zec) has until Saturday to announce the results but its chairwoman, Priscilla Chigumba, said she expected the announcement to be made well within that deadline.
"We will not subvert [the people's will]," she said at a press conference, rejecting allegations that there had been ballot rigging.
Observers say the race between Mr Mnangagwa's Zanu-PF party and Mr Chamisa's MDC Alliance is extremely tight.
Both men are among 23 candidates running for president.
Zec has announced some of the results in the parliamentary elections but says it needs time to pull together the figures for the presidential poll from across the country.
A presidential candidate needs more than 50% of the vote to win outright. Otherwise, a run-off election will be held on 8 September.
In a tweet, Mr Mnangagwa expressed confidence about his chances but added that he was "waiting patiently for official results as per the constitution".
Good morning Zimbabwe. I am delighted by the high turnout and citizen engagement so far. The information from our reps on the ground is extremely positive! Waiting patiently for official results as per the constitution.— President of Zimbabwe (@edmnangagwa) July 31, 2018
'Anxiety creeps in'
By Pumza Fihlani, BBC News, Harare
The electoral commission held two press conferences on Tuesday in a bid to keep the public informed.
But it is the result of the presidential election that people want to know, and that will not be ready for another few days.
There were more than 10,000 polling stations, and collating the votes will not be an easy task.
In the meantime, accusations are surfacing and anxieties are starting to creep in.
On the sidelines of the jostling of the politicians, the fake news media machine has kicked into full gear, with social media accounts, purporting to belong to politicians, claiming victory for their parties.
While the voting process was peaceful, the waiting and any perceived delays could raise the temperature here.
The commission has told South Africa's public broadcaster that it is under no "political pressure", implying that it will not be rushed.
But in the age of social media, where false stories thrive in an information vacuum, it does raise questions about how democracies can respect the electoral process without creating room for the very credibility of that process to be jeopardised.
Do we know any results?
Zimbabweans voted for a new president, parliament and local councils, and on Tuesday Zec announced the results for seven parliamentary constituencies.
Some candidates are already accepting defeat.
Pastor Evan Mawarire, who rose to prominence in 2016 by rallying support against Mr Mugabe's government on social media, failed in his attempt to win a seat on Harare's city council.
With much respect & admiration I congratulate Jacob Mafume @JMafume of the MDC Alliance on his win of the Mt Pleasant ward 17 council seat. You ran well my friend and I wish you the best as you serve the people of Mt Pleasant & the city of Harare. pic.twitter.com/aDY30HJYXU— #ThisFlag E Mawarire (@PastorEvanLive) July 31, 2018
His #ThisFlag movement, which denounced the government's management of the economy, gained tens of thousands of followers at the time.
Lawyer Fadzayi Mahere, who has a large following on Twitter and ran a successful social media campaign, lost her bid to become an MP for a constituency in the capital.
"We consistently said that we'd win or we'd learn," she tweeted.
We consistently said that we’d win or we’d learn. We’ve learnt that it’s important to take a stand, to speak up, to participate, to innovate, to challenge, to collaborate, to step outside one’s comfort zone and to be the change. We thank you ALL for your support. #ForeverYellow pic.twitter.com/ozmOKvNCwJ— Fadzayi Mahere (@advocatemahere) July 31, 2018
Meet the frontrunners:
Emmerson Mnangagwa, Zanu-PF
- Known as "the crocodile" because of his political shrewdness - his party faction is known as "Lacoste"
- Accused of masterminding attacks on opposition supporters after the 2008 election
- Thought to be 75 years old, he promises to deliver jobs and is seen as open to economic reforms
- Survived several alleged assassination attempts, blamed on supporters of ex-President Mugabe.
Nelson Chamisa, MDC Alliance
- His skull was fractured when beaten up by state security agents in 2007
- Became an MP at 25, a cabinet minister at 31 and could become the youngest president at 40
- A recently qualified pastor, he has been using the hashtag #GodIsInIt for his campaign
- Has promised to rebuild the country's devastated economy, but has been criticised for making extravagant promises - such as the introduction of a high-speed bullet train and bringing the Olympics to Zimbabwe.
What are foreign observers saying?
European Union (EU) and US election monitors have been allowed into the country for the first time in 16 years to assess whether the elections are free and fair.
EU chief observer Elmar Brok said on Monday it was too soon to make a judgement but voting had been "very smooth" in some areas and "totally disorganised" in other areas, Reuters news agency quoted him as saying.
"There are shortcomings that we have to check. We don't know yet whether it was a pattern or whether it was a question of bad organisation in certain polling stations," Mr Brok told the AFP new agency.
As well as worries about the voters' roll, the opposition has expressed concern over the security of ballot papers and voter intimidation in mainly rural areas.
Liberia's former President Ellen Johnson Sirleaf, who was among the monitors, told the BBC that Monday's long queues showed Zimbabweans were enthusiastic about voting, without any kind of repression.
"I think this is an exciting moment for Zimbabweans to change the course of their country through their votes," she told the BBC.