The Indian capital faces possible ‘‘imminent’’ militant attacks, the United States, Australia and Britain have warned, stepping up their risk advisories to travellers to New Delhi.

New Zealand also warned of an ‘‘extreme risk’’ of terrorism in India as the nation battles to reassure visitors it can safely host the Commonwealth Games in October in New Delhi, which has been targeted before by militants.

‘‘There are increased indications that terrorists are planning imminent attacks in New Delhi,’’ the US embassy said in a statement on its website on Saturday, urging tourists to avoid half-a-dozen of the city’s popular shopping areas.

Police in New Delhi were taking ‘‘appropriate measures’’ in response to the warnings, said police spokesman Rajan Bhagat as a source said police had been put on alert.

‘‘Security is adequate,’’ Ravindra Singh, spokesman for India’s Ministry of Home Affairs, said.