But organisers of the event, which runs from 3 to 14 October, said the facilities would be excellent.
Meanwhile, police said 23 labourers were injured as a bridge being built near the main Games venue collapsed.
It is the latest setback to an event plagued by construction delays, allegations of corruption and a dengue fever outbreak in the Indian capital.
New Zealand, Scotland, Canada and Northern Ireland have demanded their teams be put up in hotels if their accommodation is not ready. Michael Fennell, the Commonwealth Games Federation president, said he had written to the Indian cabinet secretary urging immediate action.
He said "many issues remain unresolved" and the athletes' village was "seriously compromised".
Although team officials had been impressed with the international zone and main dining area, he continued, they had been "shocked" by the state of the accommodation itself.
"The village is the cornerstone of any Games and the athletes deserve the best possible environment to prepare for their competition," Mr Fennell added.
Indian media is reporting that only 18 of 34 residential towers at the village are complete
Two days before the village officially opens to the first of 7,000 athletes and officials, New Zealand chef de mission Dave Currie suggested the Games might even be cancelled.
He said toilets in the accommodation were leaking and did not flush, and there were piles of building debris in bathrooms.
Mr Currie told New Zealand commercial radio on Tuesday: "If the village is not ready and athletes can't come, obviously the implications of that are that it's not going to happen.
"It's pretty grim really and certainly disappointing when you consider the amount of time they had to prepare."
Team Scotland said in a statement that on arrival in Delhi last week their officials found "its allocated accommodation blocks were far from finished and in their view, unsafe and unfit for human habitation".
Commonwealth Games England called for "urgent" work on the facilities, raising concerns about "plumbing, electrical and other operational details".Australia's chef de mission, retired marathon runner Steve Moneghetti, said in Melbourne the hosts "have got two days to do what's probably going to take about two weeks".
As the row unfolded, 23 construction workers were injured, five seriously, as an elevated footbridge gave way near the Jawaharlal Nehru Stadium, police said.
It is not clear what caused the collapse of the walkway, which was being built to link a car park to the arena, where the Games opening ceremony is to take place.
Delhi government's Chief Secretary, Rakesh Mehta, told Indian TV the bridge was cemented earlier on Tuesday.
Lalit Bhanot, secretary general of the organising committee, said in a news conference that the athletes' accommodation needed a "deep cleaning", but everything would be ready on time.
"According to us the room may be clean, but the foreign officials may require a certain standard of cleanliness and hygiene which may differ from our standards," he said.
"We are on the job and everyone is working day and night."He added: "All other things and all other venues are ready and in the best of condition to conduct these events."
There have also been safety concerns surrounding the Games, heightened on the weekend when gunmen shot and wounded two tourists near Delhi's Jama Masjid, one of India's biggest mosques.