Swati Maliwal made the appeal in a letter to Prime Minister Narendra Modi.
It was timed to coincide with the fifth anniversary of the brutal gang rape and murder of student Jyoti Singh, 23, whose death sparked national protests.
“Nothing has changed in the past five years,” Ms Maliwal, chief of the Delhi Commission for Women, told the BBC.
“Delhi is still the rape capital. Last month, there was a brutal gang-rape of a one-and-a-half-year-old girl, and the gang-rape of a seven-year-old, and another one-and-a-half-year-old girl was raped.”
On average, she said, three girls and six women were raped in the capital every day.
India did reform its rape laws as a result of the outcry five years ago, taking steps to speed up trials and press police officers to take allegations of rape and sexual assault more seriously, reports the BBC’s South Asia regional editor. Jill McGivering.
There is more awareness and increased reporting of cases, Ms Maliwal told our correspondent – “but that hasn’t solved the problem”.
In her letter, Ms Maliwal urges the prime minister to go further and have child rapists executed within months of their crime.