Three people have been arrested in connection with the rape, joint commissioner Sanjay Beniwal told CNN. He said that the rape was committed by one of the men in the presence of two of the arrested.
The three accused and the girl's family were co-tenants, Beniwal added.
Both girls are recovering in the hospital, and are in a stable condition, according to officials.
These latest incidents come within one week of a four-year-old being raped, again in the capital. In that case, police have arrested one man for the alleged rape, deputy police commissioner Vijay Singh told CNN.
Minister criticizes Modi
When asked about the recent cases of child rape, Delhi's Chief Minister Arvind Kejriwal blasted Prime Minister Narendra Modi for his "silence" over violent sex attacks.
He demanded to be able to take control of the Delhi police, which currently reports to the Prime Minister.
"I will not remain silent. We will not allow the Prime Minister to sleep peacefully if women in Delhi do not get proper safety and the present trend of rapes continues," Kejriwal told reporters on Sunday.
Student organizations held a protest in front of the Delhi police headquarters the same day, condemning police for their "inefficiency."
In 2014, India recorded 13,766 cases of rapes on minors -- those younger than 18 years old -- according to official data. Of those, more than 1,000 cases were reported in New Delhi, the National Crimes Record Data shows.
CNN's Roshni Majumdar, Harmeet Shah Singh and Omar Khan contributed to this report
A succession of child rapes in New Delhi has prompted angry demands for the authorities to do more to stop them.
Over the weekend, student groups held a protest in front of the Delhi police headquarters, condemning police for their "inefficiency" and demanding an end to "rape culture".
An appalling case involving the gang rape and murder of a 23-year-old student in 2012 in Delhi led to demonstrations and new anti-rape laws in the country. The government doubled the maximum prison term for rape to 20 years and created special courts to prosecute cases more quickly.