Two Indian girls aged two-and-a-half and five years old were raped in separate incidents in New Delhi overnight, with at least one confirmed as a gang rape, police said Saturday.

The younger child was abducted late Friday by two men from a religious event in west Delhi's Nangloi area and sexually assaulted before being dumped in a park near her home, police and relatives said.

Pushpendra Kumar, west Delhi police chief, said they found the younger child bleeding profusely several hours after she went missing and that tests showed she had been raped at least once.

"We have launched a manhunt for the suspects. So far no one has been arrested," Kumar told AFP of the toddler's case.

In a separate incident, a five-year-old girl was gang-raped by three men in New Delhi's eastern Anand Vihar area on Friday night after being lured to a neighbour's house, police said.

"Her clothes were partially torn with blood spots all over them. Some locals saw her and she told them she was sexually assaulted," an officer from Anand Vihar police station told AFP on condition of anonymity.

"Some of the locals then barged into the house and caught them (the alleged perpetrators) before handing them over to us," the officer said. Tests later confirmed she had been subjected to multiple assaults, he said.

Both girls are undergoing medical treatment but are believed to be out of danger, police said.

"When will Delhi wake up? Till when will girls continue to be brutalized in Indian capital. Gangrape of 2.5 year n 5 year old. Shameful," Delhi Commission for Women chairwomen Swati Maliwal tweeted Saturday.

The incidents come one week after a four-year-old girl was allegedly raped and slashed with a blade before being abandoned by a railway track in the capital.

Police arrested a 25-year-old man over that attack, in which the young girl suffered severe internal injuries and had apparently been slashed with a sharp object.

The attacks add to a grim catalogue of sexual assaults in India, many of which have sparked domestic and international outrage.

The fatal gang rape of a young student on a bus in Delhi in 2012 led to an outpouring of anger over frightening levels of violence against women.

India recorded 36,735 rape cases in 2014, with 2,096 of them in Delhi.

Experts say those figures likely under-represent the true scale of the crimes.