The woman, in her early 30s, was allegedly assaulted at a luxury hotel near the central business district of Connaught Place in April.
Police said the victim had returned home without lodging any complaint and contacted them through an NGO recently.
“We have registered a case of rape and launched investigations into the allegations.
“Our teams are making efforts to arrest the accused,’’ district police Chief Jatin Narwal said.
However, he did not give further details, saying it could hamper investigations in the case.
According to reports in the domestic media, the woman alleged that her tour guide had given her a spiked drink and later raped her with four acquaintances in the hotel room.
India’s External Affairs Minister Sushma Swaraj has said those guilty would be brought to justice.
“I have also asked the Indian ambassador in the U.S. to contact the victim and assure that we will not spare the guilty,’’ she said in a series of tweets posted earlier.
Sexual violence has been a focus of public attention in India since the fatal gang rape of a student on a bus in New Delhi in December 2012.
Activists say little has changed in attitudes towards sexual assault, and attacks on women continue unabated.
In July, a 25-year-old Israeli tourist was allegedly raped in a moving car in northern India.
In 2015, five men were sentenced to life for raping a Danish tourist in Delhi in 2014. (dpa/NAN)