Placard-wielding protesters also gathered at AIIMS, where the girl is undergoing treatment, and burnt the effigy of police Commissioner Neeraj Kumar demanding his sacking.
Traffic was affected at ITO and India Gate in the evening as the number of protesters swelled.
More than 100 people, who staged protest at PHQ and near the residences of Singh and Gandhi, were detained and later released. Rapid Action Force personnel were deployed near the residence of the Prime Minister and PHQ.
Delhi has recorded 393 rapes in the first three months of the year compared to 152 during the same period last year.
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Around 15-20 members of Arvind Kejriwal-led Aam Aadmi Party (AAP) tried to stage a protest in the evening near the Prime Minister's residence but were detained by the police.
Over 100 AAP supporters had earlier protested at PHQ. Police deployed water canons at PHQ.
Women and student activists staged demonstrations near India Gate in the evening hours.