Further doubts have been cast over next month's Delhi Commonwealth Games after two athletes withdrew and others postponed travelling to the event.
The Scottish team said they would not travel until the site was "secure", while an English and Australian athlete both pulled out over security concerns.
Officials from several countries have heavily criticised the facilities, saying they are dirty and incomplete.
But Indian authorities have insisted the site will be ready on time.
Michael Fennell, president of the Commonwealth Games Federation, is travelling to Delhi where he is hoping to meet Prime Minister Manmohan Singh, who took charge of the city's preparations a month ago.
On Tuesday, a footbridge under construction near the Jawaharlal Nehru Stadium, the main Games venue, collapsed injuring 27 workers, five of them seriously.
On Wednesday, a section of ceiling at the weightlifting venue fell in, but Indian officials said it was a minor problem and "not something to be worried about".
The state of the athletes' village has also come under fire, with complaints of flooding, rooms soiled with excrement and stray dogs sleeping on some beds.
New Delhi's Lieutenant Governor, Tejinder Khanna, said cleanliness problems had been caused by particularly heavy monsoon rains, which have caused widespread flooding and killed at least 70 people in the country's north.
Lt Gov Khanna, tasked by the Indian prime minister with overseeing the clean-up operation, said special teams had been brought in to ensure the site was ready for the start of the games in 11 days.
"We are making first-rate preparations," he said.
The structures built to house athletes were world-class, he said, adding that Wednesday's footbridge collapse was due to an engineering issue which did not impact on the games' main venues.
The event has been plagued by construction delays, allegations of corruption and a dengue fever outbreak in the Indian capital.
Security fears were heightened at the weekend when two tourists were wounded by gunmen on a motorbike near the Jama Masjid mosque in the capital.
The local organising committee has said the city will be ready in time for the imminent arrival of participants.
Committee secretary-general Lalit Bhanot said some athletes might pull out because of injury or other reasons, but there would still be "a very good field".
"I can reassure everyone that the athletes will enjoy their stay in New Delhi. The stadiums are world class and so is the Games village. We will be ready by the time they start arriving this week," he told the AFP news agency.
Australia's world discus champion Dani Samuels and English world triple jump champion Phillips Idowu have both pulled out of the Games, citing health and safety concerns, and Australia's Sports Minister Mark Arbib said more athletes from his country might follow.
Two other members of the England team - Olympic 400m champion Christine Ohuruogu and 1500m runner Lisa Dobriskey - have pulled out with injuries.
But Commonwealth Games England have confirmed the first 22 members of the English team will fly to Delhi on Thursday, as planned.
Earlier, the body's chairman, Sir Andrew Foster, told the BBC that English officials were inspecting the facilities again, and that the next two days would be critical in determining whether the village would be able to accommodate all visitors.
Scotland has delayed the departure of its first delegation to the Games, saying athletes could not be sent to an incomplete and "filthy" site.
"We really need the Delhi organisers to understand the urgency of the situation," Michael Cavanagh, chairman of Commonwealth Games Scotland, told the BBC.
"We all need to be confident that we can send our athletes into an environment which is safe and secure and healthy for them and we simply won't compromise on that. We don't believe the rest of the village is a safe environment."
Wales have given the organisers a deadline of Wednesday evening to confirm whether the village and venues are "fit for purpose", after which they said they would give further advice to their athletes.
New Zealand Prime Minister John Key told reporters that any cancellation of the Games could be disastrous for the future of the event and for India's world standing. But he said he would support any individual athlete who chose to pull out.
The head of New Zealand's Commonwealth Games team, Dave Currie, earlier warned that if the arrivals of the athletes had to be pushed back, it could ultimately result in the competition being cancelled.
The Indian media has fiercely criticised the preparations for the Games, describing visitors' comments as a national embarrassment.
The Times of India said the country had been "shamed globally" and called for those responsible for the problems to be "identified and brought to book".
On Tuesday, Mr Bhanot said the authorities understood the concerns, but suggested that the complaints from foreign delegations could be due to "different standards about cleanliness".
Built alongside the monsoon-swelled Yamuna River in the east of Delhi, the Commonwealth Games village consists of a series of blocks of flats to house about 7,000 athletes and their families, a 2,300-seat cafeteria, and practice areas.
India's Ministry of Sport promised last year that the village would be ready in March 2010.
The BBC's Mark Dummett in Delhi says there is increasing anger in India over the apparent mismanagement of the event.
The country has invested so much it is unlikely the Games will be cancelled altogether, says our correspondent, but with athletes pulling out and reports of poor ticket sales, the question being asked is what sort of Games they will be.
World Have Your Say will be in Delhi on Wednesday discussing whether the Games should go ahead. The programmes will be broadcast live on BBC World Service radio weekdays at 1700 GMT (1800 GMT in Africa).