Riot police have been out in force amid rising tensions across the country.
More than 50 Zimbabwean opposition supporters have been arrested after staging a strike, the party says.
Police have accused the Movement for Democratic Change (MDC) of trying to incite violence with their strike call, in protest at delayed poll results.
Correspondents say the strike had little impact as 80% of Zimbabweans are without a job.
The poll crisis is also likely to be raised at a UN Security Council session to be attended by some African leaders.
South African’s leader Thabo Mbeki called for the special meeting, which is supposed to be about how the UN can work with the African Union to bring peace to the Africa’s conflicts, from Somalia to Sudan’s Darfur region.
We, the neighbours are doing something about Zimbabwe, you may not agree with it but we are doing something.
Zimbabwe is not officially on the agenda.
The BBC’s Laura Trevelyan at the UN says the UK’s Prime Minister Gordon Brown, along with officials and ministers from the US and France, are expected to raise the continuing stalemate in Zimbabwe – in public and in behind-the-scenes meetings.
But Mr Brown will now not be meeting Mr Mbeki privately, say South African diplomats citing scheduling issues.
Meanwhile, a Zimbabwean judge has cleared New York Times correspondent Barry Bearak and a British national of charges of reporting on the 29 March election without proper accreditation.
Magistrate Gloria Takundwa said the state failed to prove “reasonable suspicion of them practising as journalists”.
The MDC’s spokesman Nelson Chamisa said the more than 50 arrests were countrywide – relating to minor skirmishes in townships around the capital, Harare and Bulawayo.
Mr Mbeki prefers to use quiet diplomacy than megaphone tactics
“We don’t know for what reason they have been arrested. There is no crime in staying away,” Mr Chamisa told AFP.
The news agency says one of those arrested is Chitungwiza MP Marvelous Khumalo.
Zimbabwean police reported arresting 30 MDC supporters for obstruction and intimidation.
Those arrested were found either “barricading roads and stopping people from going to work”, “obstructing the free movement of traffic” or intimidating people who went to work, police said.
The MDC’s national executive is meeting to decide whether to continue with further strike action.
They had wanted people to stay at home until the presidential election results were released.
But local journalist Brian Hungwe in Harare says most banks, shops and offices opened as usual and armed police and soldiers were on patrol.
MDC Secretary General Tendai Biti told the BBC on Tuesday that two of its activists had been killed and 200 hospitalised after being assaulted by ruling party militias.
The Commercial Farmers Union says more than 130 farms have now been affected by the recent wave of farm invasions.
About 30 white farmers are still trying to get back to their properties, while others are said to be facing repeated harassment and abuse, despite police intervention.
The election commission says it cannot release the results until a recount in some areas is completed at the weekend.
Independent counts suggest MDC leader Morgan Tsvangirai won the election but took less than 50% of the vote, meaning he would face a run-off.
His party says he will not contest a run-off unless there is a secure environment, with thorough international monitoring.
Our correspondent says that, as the Security Council meets, activists will fly a 3,000 sq ft banner above the UN, calling on President Mbeki to use his influence with Zimbabwe’s leader Robert Mugabe.
Mr Mbeki, who is chairing Wednesday’s UN session and is the appointed regional mediator for Zimbabwe, would prefer the issue to be kept out of the limelight.
The South African ambassador to the UN, Dumisani Khumalo, said he felt there was no need for Zimbabwe to be discussed on the UN platform.
“We, the neighbours are doing something about Zimbabwe, you may not agree with it but we are doing something,” he told the BBC’s Network Africa programme.
But US ambassador to the UN, Zalmay Khalilzad, disagreed that a discussion was not necessary.
“It would be very surprising that we will have a meeting on Africa in which quite a number of African leaders will be there and not talk about the most important issue, the most urgent issue on that continent, being Zimbabwe.”