NEW DELHI  Skepticism about India’s preparedness for the Commonwealth Games deepened Tuesday after a partly constructed footbridge collapsed outside the main arena for competition, injuring dozens.

The collapse coincided with angry words from visiting officials who described the accommodations for athletes as uninhabitable. One visitor, the head of the New Zealand delegation, even raised the possibility that the games might be delayed or canceled.

India’s failure to complete the work for the games, which are to begin Oct. 3 and last for two weeks, has become a major embarrassment for the country instead of a showcase for its rising economic might. The unspoken comparison to India’s rival China, which won widespread acclaim from its preparations for the 2008 Summer Olympics, are a further source of humiliation.

Representatives of the dozens of countries participating in the Commonwealth Games, a quadrennial competition among the nations of the former British Empire, started arriving here in recent days to inspect facilities and conduct security checks. The athletes’ village, built for the games, is not ready, they say, and questions linger about security after an attack on tourists in Delhi on Sunday.