The attack is the latest crime to focus attention on the scourge of sexual violence in India.
The woman also was robbed and beaten in the attack, which happened Tuesday near Connaught Place, Bhagat said.
The woman asked the men for directions to her hotel, Bhagat said. They lured her to a secluded area where they raped her at knife-point, according to the Press Trust of India news agency.
The woman managed to reach her hotel Tuesday evening and the owner called police. Police were questioning several other suspects.
"When she came, it was miserable," said Amit Bahl, owner of the Amax hotel in the Paharganj area, which is popular with backpackers. The woman was crying and "not in good shape," he said.
"I am really ashamed that this happened," said Bahl, who sounded shaken.
A sign outside the hotel reads, "Recommended by Lonely Planet."
The woman, whose name was not released, was on her way back to Denmark, said Ole Egberg Mikkelsen, head of the Danish Foreign Ministry's consular department in Copenhagen, which handles cases involving Danes abroad. Egberg Mikkelsen said the woman had received assistance from Indian and Danish authorities, and that her next of kin had been contacted.
An Indian police official said the woman boarded a flight home Wednesday morning.
It was not immediately known whether she had been traveling alone. The Danish Embassy in New Delhi had no comment.
The problem of sexual violence in India has gained widespread attention since the horrific gang rape and murder of a 23-year-old woman on a moving bus in December 2012. Public fury over the case has led to more stringent laws that doubled prison terms for rape to 20 years and criminalized voyeurism and stalking.
But for many women, particularly the poor, daily indignities and abuse continue unabated and the new laws have not made the streets any safer. Ranjana Kumari, director of India's Center for Social Research, said India's conservative, patriarchal traditions lead men to use rape as a tool to instill fear in women.
"This mindset is not changing," she said. "It's a huge challenge."
Experts say the rapid growth of India's cities and the yawning gulf between rich and poor are exacerbating the problem of sexual violence, with young men struggling to prove their traditional dominance in a changing world.
Cultural stigmas, police apathy and judicial incompetence have long made it difficult for women to even report rapes.
Still, there has been a surge in the number of rapes being reported recently, suggesting women are emboldened to speak up. Between January and October last year, 1,330 rapes were reported in Delhi and its suburbs, compared with 706 for all of 2012, according to government figures.
Foreigners also have been targets, including a Swiss woman who was cycling with her husband in central India when she was gang-raped.
The cases threaten India's lucrative tourism industry. Last year, the Tourism Ministry launched an "I Respect Women" campaign to reassure travelers. Tourism accounted for 6.6 percent of India's GDP in 2012, the latest year for which figures are available.
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