The bill may go to a higher body, the Expediency Council, for review.
The former president, who heads the powerful Expediency Council, has often used his influence against reformers.
If Parliament persists in its support, the bill would go before the Expediency Council for final arbitration.
He died on the 16 February 2008, from a heart attack, while delivering a speech to the Expediency Council.
If the two branches of government cannot agree, the bill will go to a mediating body, the Expediency Council, which is also controlled by conservatives.
After this, he has tried to use his position in the Expediency Council to denounce President Ahmadinejad's administration.
The Parliament can appeal, but only to another potentially unfriendly body called the Expediency Council.
He is also senior member of Iran's Expediency Council.
In 1991, Rouhani was appointed to the Expediency Council and has kept that post up to the present time.
He will continue to hold considerable power as head of the Expediency Council, a powerful body charged with mediating between political and religious leaders.