Australia and the United States have issued travel warnings for India, a day after two Taiwanese tourists were wounded by gunmen near the main mosque in the capital Delhi.
A car exploded near the mosque minutes after the gunmen opened fire on a tourist bus on Sunday. Officials say the two incidents may have been connected.
Interior ministry officials on Monday played down the shooting, saying it could be the work of local criminals.
However a government source says militant action cannot be ruled out.
Both Australia and the United States urged their citizens to be careful.
The government has directed the police to tighten security across the city, which will host the Commonwealth Games. The event is due to run from 3 - 14 OCtober.
An email purportedly from the Indian Mujahideen, a home-grown Islamist group with links to others in Pakistan, was sent to the BBC and some domestic media after the attack. The statement threatened attacks on the Games.