Delays are fuelling suspicions of vote-rigging (AP)
Some voters spent the night in the open, wrapped in blankets, waiting for the polling stations to re-open. One station in Harare stayed open all night to cope with the large turnout.
Some 5.6 million people are eligible to vote in the election, in which President Robert Mugabe faces a strong challenge to his 22-year rule from Morgan Tsvangirai, leader of the opposition Movement for Democratic Change (MDC).
Mr Tsvangirai cast his ballot on Sunday - his 50th birthday - and renewed calls for a two-day extension of the vote.
"If the authorities refuse to extend it would be a tragedy for this country," he said. "People have expressed themselves and we are awaiting the outcome."
Mr Tsvangirai's MDC party on Sunday said it had filed an urgent application to extend the vote with the High Court, which was due to hear the request at 1400 (1300 GMT).
Zimbabwe's Justice Minister, Patrick Chinamasa, has said that polling would be extended "if it becomes necessary".
Clashes
Tempers were wearing thin among those queuing to vote by the time polling officially ended on Saturday at 1700 GMT, and at one station in Harare voters angry at the long wait clashed with police.
Click here to tell us your experiencesReports on Sunday said the wait to vote appeared more orderly after police ordered voters to queue in single-file, men standing separately from women.
State radio reported that electoral officials planned to add voting booths to the polling stations to alleviate the wait.
Zimbabwe votes:
"I wasn't going to go away. I must have my vote," she said.
Reginald Matchabe-Hove, chairman of independent observer group the Election Support Network, said only 30% of those who queued to vote on Saturday had voted.
"There is no way this can be completed in two days," he said.
Mr Mugabe's spokesman, George Charamba, said the government was "perfectly happy" with Saturday's ballot and was not concerned by complaints of slow voting.
Correspondents say last-minute changes to the election laws, changes to the voter register and a reduction in the number of polling stations in urban areas, have slowed the process dramatically.
Sanctions
After casting his vote on Saturday, Mr Mugabe hit out at his critics - at home and abroad.
"They are supporters of the opposition. It is not only prejudice, it is bias against the [ruling party], bias against President Mugabe, and bias in favour of the opposition."
In the run-up to the election, the European Union and United States imposed sanctions on Mr Mugabe and his aides, citing political violence and manipulation of the election process.
Within the region, the poll is seen as crucial for Zimbabwe's neighbours, as the country's economic crisis has hit trade - depriving South Africa of multi-million-dollar foreign investment - and created a new refugee problem.
Mr Mugabe's opponents say misrule and controversial land grabs by his supporters are largely to blame for the economic crisis.