A Zimbabwean journalist said militias loyal to Mr Mugabe had gone door-to-door in townships outside the capital, Harare, forcing people to vote.
The BBC's John Simpson, in Harare despite a reporting ban, says he had never seen an election as frightening - where people know that if they fail to turn out to vote and do not have the ink stain to prove it, they are liable to the most ferocious retribution from the ruling Zanu-PF.
He adds that if someone summoned up the courage to vote for Mr Tsvangirai - whose name is still on the ballot - there were fears their identity could be discovered.
Journalist Themba Nkosi, in Bulawayo said officials for Mr Tsvangirai's Movement for Democratic Change (MDC) had told supporters in rural areas to vote if they felt their lives were in danger - and to vote for Morgan Tsvangirai or spoil their ballot.
A resident of Manicaland Province told the BBC: "I am not going to vote in a one-person race. I will not vote for a dictator and for hunger while my brother was killed in cold blood."
Zimbabweans explain why they are voting in the election
But Zanu-PF supporter Richard Munsaka, in Hwange, Matebeland North Province said the question of a free and fair election "depends on the eyes of the beholder".
"I'm not saying there is no violence in the east of the country... but not on a massive scale and that in itself cannot stop the whole country from going to vote just because a few individuals are kicking themselves."
A woman in Harare said as she prepared to vote: "I will be exercising my right. We as Zimbabweans need to decide the direction that we want the country to take - so we can only do that by voting."
At a news conference held in Harare before polls closed, Mr Tsvangirai said people were being intimidated into voting but said millions were refusing.
Mr Mugabe came second to Mr Tsvangirai in the first round of the presidential vote - also held in March.
Since then, the MDC says some 86 of its supporters have been killed and 200,000 forced from their homes by militias loyal to Zanu-PF.
The government blames the MDC for the violence.
Regional leaders - including from Nigeria, the Southern African Development Community (Sadc) and the African Union - had called on Mr Mugabe to postpone the vote and negotiate with the opposition.
While Mr Mugabe said he planned to attend an African Union summit in Egypt next week, Mr Mugabe said the AU had "no right in dictating to us what we should do with our constitution, and how we should govern this country".
He has suggested negotiations with the MDC were possible - "should we emerge victorious, which I believe we will".
Mr Tsvangirai has said negotiations would not be possible if Mr Mugabe went ahead with the run-off.
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