Australia's Olympic Committee president has said the Commonwealth Games should not have been awarded to Delhi.
John Coates also said the Commonwealth Games Federation lacked the resources to monitor progress and to ensure that construction deadlines were met.
England have become the first overseas team to reach Delhi, but other nations have delayed their arrivals.
A New Zealand cyclist became the first member of his nation's team to pull out because of health and safety fears.
Greg Henderson, who has won four medals at previous Games cited concerns over the state of facilities - a day after four British cyclists withdrew from the 3-14 October competition.
On Thursday, the BBC obtained pictures showing flooding, leaking toilets, dirty bathrooms, incomplete apartments and paw prints on beds in the athletes' village.
Delhi Games organisers have drafted in staff from the city's five-star hotels to help the last-minute scramble to get the accommodation ready.
The build-up to the event has been marred by construction delays, corruption scandals, a dengue fever outbreak, the collapse of a footbridge near the main stadium and security fears after Sunday's shooting of two tourists outside Delhi's Jama Masjid mosque.
"The Games shouldn't have been awarded to Delhi in hindsight," Mr Coates told Australian radio.
"The problem is the Commonwealth Games Federation is under-resourced. It doesn't have the ability to monitor the progress of cities in the way the [International] Olympic Committee does."
Nevertheless, Australian Commonwealth Games officials said that having visited the athletes' village on Friday, their team were "quite happy" with the accommodation and would move in on Monday.
The first English athletes - the men's hockey and the bowls teams - arrived in Delhi on Friday, although they plan to stay in hotels until Monday, when the village should be ready.
New Zealand announced on Friday it would send its team to compete in Delhi, although it would continue to review the situation daily.
Scotland said its team would fly to Delhi on Saturday. The Welsh team is on its way, too, and Canadian officials were hopeful the first of their athletes could arrive on Sunday.
Kenya has said it will send its team to the Games, after receiving security assurances from India.
Commonwealth Games Federation president Mike Fennell said in a statement that "considerable improvements" had been made to the athletes' village.
But he added: "It is vital that all remedial work that has already started continues with the greatest urgency."
The first athletes, from India's team, have just moved into the accommodation.
Indian Prime Minister Manmohan Singh has taken control of the crisis.
He held talks on Thursday night with his sports minister and Delhi officials.
Games organising committee chairman Suresh Kalmadi, whose team has been mired in corruption allegations, was not invited.
Other athletes who have pulled out because of health and safety fears include Australian world discus champion Dani Samuels and English world triple jump champion Phillips Idowu.
Ticket sales have been low, and the cost of hosting the largest sporting event in India's history has soared.
It has become most expensive Commonwealth Games so far, with estimates ranging up to more than $10bn (£6.3bn).
Delhi has had seven years to prepare, though very little work was done until 2008.