Mulayam Singh Yadav, an SP leader, said: "We are not anti-women but we want reservations for women hailing from minority and backward classes first."
The vote had been scheduled for Monday to coincide with International Women's Day, but has now been stalled until at least Tuesday.
The bill seeks to provide 33 per cent reservation to women in parliament and state legislatures and has been championed by both Manmohan Singh, the Indian prime minister, and Sonia Gandhi, the Congress party chief.
The opposition Bharatiya Janata Party (BJP) has also publicly pledged their support.
But the bills critics say the legislation, which was first introduced 14 years ago but has been consistently blocked, will be passed at the expense of other minority groups such as Muslims or lower castes.
The also argue it will only benefit women already in privileged classes.
A UN report, released on Monday, said that the Asia-Pacific region ranks near the bottom on many women development issues such as political representation, impacting the growth prospects of developing nations.
Separately, the government's loss of support from the SP and RJD, which combined account for 26 seats in the 545-seat lower house, could hinder Congress's ability to push through legislation on economic reforms.
Since winning a second term last year, Congress is already under fire over a number of issues, including a fuel price increase announced in the February budget.
"Certainly the party will be weakened for future legislation," Amulya Ganguli, a political analyst, was quoted by the Reuters news agency.
"The government will need every vote it can."