It will have to be approved by 15 of India's 28 states and require presidential consent before it becomes law.
Arun Jaitley, a top leader of the conservative Bharatiya Janata Party, said women had only 10 per cent representation in powerful lower house of parliament.
The proposal is an attempt to correct some of the gender disparities in India, where women receive less education than men and are weighed down by illiteracy, poverty and low social status.
The bill would raise the number of female legislators in the 545-seat lower house to 181 from the current 59. It would nearly quadruple the number of
women in the 250-seat upper house.
Its reintroduction to parliament on Monday coincided with International Women's Day.
But politicians opposed to it forced repeated adjournments and at one point ripped up the law, threw shreds of paper at the speaker and grabbed his microphone.
Socialist politicians have argued that the bill does not go far enough.
They are calling for seats to be reserved for ethnic minorities and people from low castes.