Parliament's judicial commission voted to scrap two articles, including one relating to polygamy, in the Family Protection Bill, committee spokesman Amin Rahimi told Iran News Network's website.
Article 23 required men simply to obtain a judicial permit to remarry to confirm they can provide financially for the new wife and that both wives will be treated equally.
Under current legislation, a man in most cases has to prove his first wife's consent for another marriage.
The second article, 25, imposed taxes on the dowry, the money or property pledged by the man to his bride, which she can claim at any time through the course of marriage or when getting a divorce.
Iran's judiciary, which had originally drawn up the bill, said the two disputed articles had been added by the government.
Rahimi said the revision was ordered by parliament speaker Ali Larijani after "clerics, religious people and women expressed sensitivities" about the bill, which is yet to be adopted by the house.
"We hope today's changes alleviate concerns in the society and Iranian women can raise their children and strengthen the foundation of family with relief," he added.
The new bill had sparked strong criticism in Iran, where polygamy remains relatively rare compared with some Muslim countries and is frowned upon by many.
Many women, regardless of their reformist or conservative leanings, slammed the bill, saying it paves the way for rich men to take a second wife and "threatens the foundation and sanctity of the family."
Iran's Nobel peace laureate Shirin Ebadi said the bill would bring "moral corruption" to society and appeared in parliament last week along with dozens of rights advocates to urge MPs to reconsider the bill.