Western governments have persistently warned of the threat of a militant attack during the Games, which run until October 14.
Delhi police commissioner Y.S. Dadwal promised "foolproof security" but called the Games a "moment of challenge" and urged citizens to be on guard.
Every police officer "is on the job 24/7. Most are working and sleeping at the police station," he told a news conference on the eve of the Games.
Dadwal's statements came as US Central Intelligence Agency chief Leon Panetta made a stopover in New Delhi to discuss the Games and regional security threats after visiting Pakistan for talks, the Press Trust of India reported.
Britain's Prince Charles, sent by Queen Elizabeth to represent her at the Games' opening ceremony, arrived in the capital.
The 84-year-old monarch, the ceremonial head of the Commmonwealth, is giving the event a miss for the first time, pleading a hectic schedule.
India was deeply embarrassed by revelations about rampant corruption