Turnouts of more than 100% were recorded in at least 30 Iranian towns in last week's disputed presidential election, opposition sources have claimed.

In the most specific allegations of rigging yet to emerge, the centrist Ayandeh website – which stayed neutral during the campaign – reported that 26 provinces across the country showed participation figures so high they were either hitherto unheard of in democratic elections or in excess of the number of registered electors.

Taft, a town in the central province of Yazd, had a turnout of 141%, the site said, quoting an unnamed "political expert". Kouhrang, in Chahar Mahaal Bakhtiari province, recorded a 132% turnout while Chadegan, in Isfahan province, had 120%.

Ayandeh's source said at least 200 polling stations across Iran recorded participation rates of 95% or above. "This is generally considered scientifically impossible because out of every given cohort of 20 voters, there will be at least one who is either ill, out of the country, has recently died or is unable to participate for some other reasons," the source said. "It is also unprecedented in the history of Iran and all other democratic countries."

The claims are impossible to verify, but they are consistent with comments made by a former Iranian interior minister, Ali Akbar Mohtashamipour, who said on Tuesday that 70 polling stations returned more completed ballot papers than the number of locally eligible voters.

Supporters of the defeated reformist candidates, Mir Hossein Mousavi and Mehdi Karoubi, have complained that their campaigns' inspectors were refused access to or ejected from polling centres on election day.

Abbas Abdi, a Karoubi supporter who was among the radical students who took over the US embassy in Tehran in 1979, said some polling stations had run out of ballot papers as early as 10.30am – even though it is standard procedure to issue each voting centre with more ballots than the number of voters.

After polling times were extended beyond the original 6pm closing time, other stations refused to provide ballot papers for fear that participation would exceed the number of voters on the register, Abdi told Radio Zamaaneh, a Farsi-language station based in the Netherlands.