New Zealand is the latest country, after Canada and Scotland, to delay the arrival of its athletes in Delhi for the event which begins on 3 October.
Indian PM Manmohan Singh is meeting key ministers to discuss progress, his office said.
Games chief Michael Fennell is also due in Delhi for emergency talks.
India insists the Games will be one of the most successful ever, but several participating countries have delegates in the capital urgently checking the facilities and arrangements for security. Two athletes have pulled out citing safety concerns.
The athletes’ village, which will house some 7,000 participants, will be open to guests on Thursday but is still unfinished.
The BBC has obtained pictures from inside the village showing flooding, leaking toilets, dirty bathrooms, incomplete apartments and animal paw prints on beds.
The BBC’s Mark Dummett in Delhi says that 1,000 extra people have been sent into the village to clear things up, but that time is running out.
Concerns have also been raised about the state of the sporting arenas, after a small section of ceiling at the weightlifting venue fell in and a pedestrian bridge at the main stadium collapsed, injuring 27 construction workers.
Security fears increased after the shooting of two tourists near one of the city’s top tourist attractions over the weekend.
Mr Singh is meeting ministers involved in the Games on Thursday. A spokesman for his office told the AFP news agency the Games would be “the only point of discussion on the agenda”.
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Dirty sink in athlete’s village
Mr Fennell is due to arrive in Delhi on Thursday and is believed to have requested a meeting with Mr Singh, who took charge of the event last month.
The chief executive of the Games, Mike Hooper, said there had been improvements every day in the state of the facilities but that there was still more work to do.
“Everybody wants to make this work, and everyone is working together to make this happen,” he told the Associated Press news agency.
Most countries planning to take part in the Games say they have no plans to reschedule or cancel their arrival in Delhi.
But several have expressed their concern about the city’s readiness to cope with the influx of visitors.
The president of the New Zealand Olympic Committee (NZOC), Mike Stanley said the conditions are “tremendously disappointing” and that his country may not send its athletes to the Games until 28 September.
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Where Key Countries Stand
“The long list of outstanding issues has made it clear the village will now not be ready for New Zealand athletes to move in as planned,” he said.
Commonwealth Games Canada (CGC) president Andrew Pipe said he was “cautiously optimistic” progress was being made.
But he added: “It’s incomprehensible that Indian officials have been so indifferent in preparing these facilities, bordering on the intransigent, and that is unacceptable to us.”
Australia’s Commonwealth Games chief Perry Crosswhite has written to all Australian athletes due to take part to assure them that safety measures at the Games are “extensive and well organised” and that the security risk was “at an acceptable level”.
Prime Minister Julia Gillard said Australia had “boosted the number of officials” in Delhi and had others on standby, while Sports Minister Mark Arbib said that the current policy of leaving the decision on whether to attend to the athletes “could change”.
Scotland put back the departure of its first delegation of athletes but Sports Minister Shona Robinson says she has “growing confidence” that the team will take part in the Games.
Australia’s world discus champion Dani Samuels and English world triple jump champion Phillips Idowu have both pulled out of the Games, saying they were concerned for their safety.
Sir Andrew Foster, chairman of Commonwealth Games England, said on Wednesday that the Games were on a “knife-edge”: “We remain very concerned about the situation and we will monitor it on an absolutely regular day-by-day basis.”
Julia Gillard has told Australians to exercise “a high degree of caution in India”
The team remained “intent on going”, he added, but “all options remain open”.
Singapore’s Games chief executive said he was in Delhi to monitor the situation and that the time was “critical”.
On Wednesday, Indian Foreign Minister SM Krishna told the BBC that the Games would meet international standards.
Mr Krishna said a prolonged monsoon had hampered preparations, but offered reassurance that security would be provided for every athlete and venue.
Ticket sales have been disappointing and the cost of hosting the largest sporting event in the country’s history has soared, making it the most expensive Commonwealth Games so far, with estimates ranging from $3bn (£1.9bn) to more than $10bn (£6.4bn), as organisers attempt to complete work which only began in 2008. -BBC