Varun Gandhi wrote to party chief Nitin Gadkari, opposing the legislation saying that such a step will drive a wedge between sections of society.
Tandon said an all-party meeting should reconsider the matter.
On Friday, the last day of the winter session of Lok Sabha, the BJP refused to back the measure, arguing that the original text had undergone changes and more time was needed to study it.
Led by LK Advani, senior BJP leaders Sushma Swaraj, MM Joshi and Rajnath Singh appear to favour that the bill,which was passed by Rajya Sabha, should be referred for a review by the Supreme Court.
Leader of opposition in Rajya Sabha Arun Jaitley had supported the bill after the government assured in the House that the rules under the law would ensure that merit was not affected in this regard.