Zimbabwean president Robert Mugabe's political opponents went to court on Friday to challenge his victory in last week's elections and demand an immediate rerun.

Lawyers for the Movement for Democratic Change (MDC) filed papers at the constitutional court alleging that the polls were rigged in favour of 89-year-old Mugabe's ruling Zanu-PF party.

Mugabe, Africa's oldest leader, won with 61% of the presidential vote, trouncing MDC leader Morgan Tsvangirai on 34%. Zanu-PF gained more than a two-thirds majority in parliament, with 160 seats compared with 49 for the MDC.

The African Union and most southern African nations have generally been supportive of the vote, but sharp criticism has come from non-governmental groups and western governments including Britain. Botswana has also called for an audit.

Few analysts believe the MDC will make much headway in court, however, noting that judges are appointed by Mugabe and generally favour the ruling party.

There have been no significant protests against the result as Mugabe retains an iron grip. Police trucks with mounted water cannon watch over "freedom square", the name given to an open field in downtown Harare by MDC supporters who held what was described as the country's biggest ever election rally there.

The MDC has also accused the police of a round-the-clock heavy deployment and surveillance by armed police at its Harvest House headquarters in Harare, describing it as "a clear sign of provocation intended to intimidate, instil fear and subdue any dissension".

"The MDC views this is as a wanton act of aggression by Zanu-PF aimed at covering up the massive electoral fraud by the Zimbabwe Electoral Commission (ZEC) orchestrated at the behest and connivance of Zanu PF," the party said.

"The MDC finds it strange that the police and Zanu-PF are using such intimidatory tactics when Zanu-PF is claiming that it won last week's elections. We wonder why the victor should be afraid of the people and the actions by the police vindicate the MDC's position that Zanu-PF using ZEC stole the people's victory.

"The heavy deployment of police at Harvest House clearly shows that Zanu PF is hiding something."

On Thursday, Zimbabwe's state election commission admitted that nearly 305,000 people were turned away from voting and another 207,000 were "assisted voters" –" supposedly illiterate or infirm" – who needed help from polling officials to cast ballots. But it insisted the mistakes were not enough to affect the outcome.

The MDC seized on the figures, however, claiming they vindicate its position that the elections were a "monumental farce" that "stole the people's victory". It noted that highest number of votes turned away was in Harare province – an MDC stronghold.

It added: "However, although ZEC has released these figures, the correct numbers are higher than this considering that two million people particularly in the urban areas failed to register in the chaotic voter registration exercise.

"From the figures released by ZEC, it is clear that people's will was disregarded especially in the rural areas where villagers were coerced to vote for Zanu-PF by the state agents, Zanu-PF militias and traditional leaders in clear violation of the electoral act."

The MDC demanded a forensic audit of the electoral processes and a rerun of a free and credible election as soon as possible. But Zanu-PF has poured scorn on the complaints as sour grapes.

Patrick Chinamasa, justice minister and a member of the party's legal team, said last week: "Start preparing your case if you have any. Feel free to employ the best lawyers; I know that you have very good lawyers at the MDC. If you are dissatisfied with what happened, the courts are there. This is why we set them up and we have instructed them to give decisions expeditiously."

Amnesty International claims that some female political activists in rural areas say they have been threatened with violence and forced to flee with their children for refusing to reveal their vote to supporters of Zanu-PF. The women said they resisted instructions from Zanu-PF supporters to feign illiteracy, blindness or physical injury, which would have meant someone else marking the ballot on their behalf.

Noel Kututwa, Amnesty's deputy director for Africa, said: "It appears the Zanu-PF supporters wanted to ensure that these women did not vote for the other parties and tried to compromise the secrecy of the ballot.

"The Zimbabwean police must guarantee the safety of political activists in rural areas following these reports of politically motivated displacement. The authorities have a duty to investigate any threats of violence and ensure those responsible are brought to justice."