HARARE (AFP) - Crisis-weary Zimbabweans flocked to cast their ballots on Wednesday in a fiercely contested election overshadowed by accusations of vote-rigging as President Robert Mugabe bids to extend his 33-year rule.

The 89-year-old firebrand, Africa's oldest leader, is running for office for the seventh and perhaps final time, after a series of violent crackdowns, economic crises and suspect elections.

"I am sure people will vote freely and fairly, there is no pressure being exerted on anyone," he said as he cast his vote in a Harare suburb. "So far so good."

The veteran leader, a hero of Africa's liberation movement for his fight against white minority rule who then became an international pariah, had vowed on Tuesday that he would step down if he loses.

"If you lose you must surrender," he said, insisting: "We have done no cheating." Prime Minister Morgan Tsvangirai - his perennial rival and reluctant partner in an uneasy coalition for the past four years - has voiced concerns that the electoral roll has been rigged.

The 61-year-old former union leader, who was forced out of the bloody election race in 2008 after 200 of his supporters were killed, told CNN he took Mr Mugabe's promise to step down "with a pinch of salt".

US State Department spokeswoman Jen Psaki voiced doubts about the way the election would be run.

"We do remain concerned about the lack of transparency in electoral preparations, by continued partisan behaviour, by state security institutions, and by the technical and logistical issues."

Still, Mr Tsvangirai cut a confident figure as he cast his own ballot, predicting his Movement for Democratic Change (MDC) would win "quite resoundingly".

"This is a very historic moment for all of us," he said. It is the time to "complete the change."

Turnout appeared to be brisk in the urban areas where Mr Tsvangirai has enjoyed his strongest support, and which he must retain to stand any chance of victory.

Voters, some wrapped in blankets on a cold winter morning, started queing at least four hours before polling stations opened.

"I am happy to have cast my vote. I just want an end to the problems in our country," said 66-year-old Ellen Zhakata as she voted in a Harare township.

"All my children are outside the country because of the economic troubles here. I am so lonely. How I wish they could be working here."

Millions of Zimbabweans were forced to migrate to find work elsewhere after an economic collapse exacerbated by the violence-marred 2008 elections.