In the Lok Sabha, members led by Shahnawaz Hussain (BJP) raised the matter and demanded suspension of Question Hour.
But, members took their seats after Speaker Meira Kumar assured them that they would be allowed to raise it during Zero Hour.
"This is a serious issue. This is a heinous act. I will allow you to raise the matter during Zero Hour," Kumar said.
In Rajya Sabha, soon after Chairman Hamid Ansari condoled the death of over a 1,000 people in a cyclone in Philippines, almost all Opposition members were on their feet raising the issue and the law and order situation in Delhi.
M Venkaiah Naidu (BJP) said his party has given a notice for suspension of Question Hour to discuss the crime.
Ansari at that point allowed Maya Singh (BJP) to make a brief statement.
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She said yesterday's rape had crossed all limits and raised grave question mark on safety of women and law and order situation in the national capital.
Singh wanted the Home Minister to immediately come to the House and make a statement.
Minister of State for Parliamentary Affairs Rajeev Shukla rose to make a submission but was not allowed to speak by the Opposition members who persisted with their demand.
"We all are equally upset and distressed over what happened," Ansari observed, adding the issue was discussed at the morning meeting and it was agreed that the matter would be taken up at noon.
Amid uproar, he adjourned the House for 15 minutes. (MORE)