Eleven seats are still available and reformists will be hoping to pick up a handful of these.
The reformists complained after the first round that the results had not accurately reflected their performance, especially in Tehran, but the complaints were discounted by the electoral authorities.
Under Iranian election law candidates needed at least 25 per cent of the vote to be elected outright in the first round.
“The same feeling that motivated us to accomplish our duty in the first round is motivating us to vote today,” Ayatollah Ali Khamenei, Iran’s supreme leader, said as he cast his vote in Tehran.
“There an old Iranian saying that the ‘the one who does the work is the one who finishes the work’,” Khamenei, who traditionally is always one of the first to vote, said.
Although conservatives are assured of holding an overwhelming majority in the parliament, Mahmoud Ahmadinejad, the president, will not necessarily have things all his own way.
Ahmadinejad has infuriated many more moderate conservatives with his economic policies, which economists blame for Iran’s high inflation, and his increasingly virulent attacks on opponents.
Duiring the past week, Ahmadinejad has been locked in a row with Gholam Ali Hadad Adel, the parliamentary speaker, over the implementation of past legislation and has replaced his economy minister.
“The eighth parliament [since the 1979 Islamic revolution] will not be an opposition parliament but it will be a critical parliament,” Amir Mohebian, an Iranian political analyst, told the AFP news agency.
The new parliament will begin work in May.