Police roadblocks have been set up around Zimbabwe's capital, Harare
Zimbabwe could be heading for a presidential run-off within three weeks, according to the state-owned Herald newspaper.
The first official indication of the result of Saturday's election says that neither President Robert Mugabe nor his main challenger gained 50% of the vote.
Opposition leader Morgan Tsvangirai says he won the poll but denies discussing Mr Mugabe's departure.
Election officials say the verification of presidential results has begun.
They say that the votes are being verified and collated in the presence of the presidential candidates' chief polling agents in the capital, Harare.
Mr Tsvangirai said he would not claim victory until the official count was known and added that no negotiations would take place until such time.
The BBC's Southern Africa correspondent Peter Biles says it is widely believed that President Mugabe would not want to face the humiliation of a run-off, should neither he nor Mr Tsvangirai obtain an absolute majority this time.
Correspondents say Mr Mugabe would be unlikely to win a run-off, as those who voted for independent candidate Simba Makoni would be expected to vote against the president.
Deputy Information Minister Bright Matonga also rejected reports of discussions paving the way for Mr Mugabe to step down.
Opposition Movement for Democratic Change (MDC) sources had earlier told the BBC the outline of an agreement had nearly been reached for Mr Mugabe to leave office.
The BBC's Ian Pannell in Zimbabwe, despite a ban on BBC reporters there, says the process is so sensitive that nobody wants to conduct it in public.
In the separate parliamentary race, results released so far show that the MDC has 96 seats, including five for a breakaway faction of the party, against 93 for Zanu-PF, with 21 still to come.
In his first public appearance since the election, Mr Tsvangirai told a news conference on Tuesday evening there was "no way the MDC will enter in any deal before ZEC [Zimbabwe Electoral Commission] has actually announced the result".
But he said the MDC would issue its own tally of presidential results if ZEC continues to withhold the official figures.
Zimbabweans are anxious to know the results
They would be based on the figures which had to be posted by law outside each polling station after counting was completed.
Many results have been available since Sunday.
Quoting analysts, The Herald newspaper said on Wednesday that the "pattern of results" indicated by the parliamentary tight race showed a re-run would be necessary.
The Herald is generally seen as reflecting government thinking.
Independent observers had previously said Mr Tsvangirai seemed to have taken the most votes in the presidential race.
More than 50% of the vote is needed to avoid a second run-off vote, which would have to be held three weeks after the 29 March election.
While the atmosphere on Zimbabwe's streets remains peaceful, if tense, there are fears that prolonging the declaration of results could lead to violence.
Roadblocks have been set up around the capital, Harare, and there has been a marked increase in the presence of paramilitary police on the streets of major cities.
Trained as a teacher
1961: Married Ghanaian Sally Hayfron
1964: Imprisoned by Rhodesian government
1980: Wins post-independence elections
1980s: Accusations of atrocities in south-west
1996: Marries Grace Marufu
2000: Loses referendum
2000: Land invasions start
2002: Wins presidential elections, dismissed by western observers
2008: Runs for a sixth term as president
As pressure grew around the world for final results to be declared, United Nations Secretary General Ban Ki-moon called for calm.
He urged the "utmost transparency be exercised so that the people of Zimbabwe can have full confidence in the process".
The White House said it was clear the people of Zimbabwe had "voted for change".
UK Prime Minister Gordon Brown called for the results of the presidential election to be published as soon as possible.
"What we want to see is that the whole of the Zimbabwean people can be guaranteed that the elections are fair and are seen to be fair, and we get the democratic outcome that the people of Zimbabwe have chosen," he said.
South African Archbishop Desmond Tutu told the BBC the fact that results had not been announced was very significant.
"Even the dumbest of us would say that results would not have been held back... had it not been the fact that Mr Mugabe has not won," said the Nobel Peace Prize winner.
Earlier the Zimbabwe Election Support Network, a coalition of civil society organisations, said its random sample of poll stations indicated Mr Tsvangirai had won just over 49% of the vote and Mr Mugabe 42%.
Mr Makoni, a former Mugabe loyalist, trailed at about 8%.
Two senior ruling party sources had told Reuters news agency that their projections were similar - indicating a run-off would be needed.
Mr Mugabe, 84, has not been seen in public since the election but Mr Matonga has denied rumours the president had left the country.
He came to power 28 years ago at independence but in recent years Zimbabwe has been plagued by the world's highest inflation, as well as acute food and fuel shortages.