The physiotherapy student and her male companion were brutally beaten and thrown off the vehicle after the attack, which has provoked street protests and widespread anger over the treatment of women in India.
"We will seek the most severe punishment of life imprisonment for the culprits and we will send a proposal to the government for the death sentence for rapists," New Delhi police commissioner Neeraj Kumar told reporters.
Rape currently carries a maximum punishment of 10 years in prison, while the death penalty is restricted to rare cases of murder and "waging war against the country".
Four of the six alleged attackers, including the bus driver, have been arrested and a hunt has been launched for two other suspects involved in the Sunday evening assault.
Delhi Chief Minister Sheila Dikshit on Tuesday vowed to "act tough" to crack down on rape and said the suspects must face a fast-track trial.
Kumar said the suspects took the off-duty school bus for a "joy-ride" and offered to take the student and her companion, who had just watched a movie, home for a regular fare.
"They began molesting the girl and her companion bravely fought back trying to save her but these men attacked him with an iron rod," he said. "The victim was dragged to the rear of the bus and brutally beaten and raped."
The female victim was in intensive care while her companion, a 28-year-old software engineer, was also being treated in hospital for multiple injuries.
Protesters blocked traffic at the intersection in the south of the city where the couple boarded the bus, while others demonstrated outside a nearby police station.
"No more rapes or harassment," shouted protesters.
Molestation of women is a serious problem in many Indian cities, with rights campaigners complaining that the commonly-used term "eve-teasing" is a dangerous euphemism that hides a culture of abusive sexual behaviour.
The case triggered an emergency debate in parliament and made the front-pages of all newspapers, with the Mail Today headline reading "Savagery shames city".
Some lawmakers including Sushma Swaraj, leader of the main opposition BJP party, also called for rapists to be hanged.
Rape cases in India more than doubled between 1990 and 2008, according to official data.