Top officials from the New Zealand Olympic Committee have arrived in the Delhi amid increasing concerns over security and the state of facilities ahead of the Commonwealth Games.
Several big-name international athletes have already pulled out, while Scotland has delayed the departure of its team.
Part of a false ceiling at the weightlifting venue caved in on Wednesday, adding to India's woes as organisers scramble to be ready for the opening on 3 October.
No one was injured at the weightlifting venue, but it comes just a day after a footbridge collapsed by the main Jawaharlal Nehru Stadium, injuring 27 workers.
Some countries have given Delhi a few days to clean up the athletes' accommodation at the Games Village - which has been described as filthy - or they will withdraw.
An outbreak of the mosquito-borne disease dengue fever is also concerning athletes.
The first New Zealand athletes are due to fly to India on Saturday, but the team's chef de mission Dave Currie has doubts the Games will be able to start on time.
Members of NZOC are already in Delhi and were joined by president Mike Stanley and secretary-general Barry Maister on Wednesday after Mr Currie described the athletes' accommodation as uninhabitable.
New Zealand officials have been inspecting the Games Village and the athletes are putting their faith in them to make the right choice about whether they should compete.
The officials will meet on Friday to discuss whether they are satisfied with security arrangements. New Zealand Prime Minister John Key says athletes have his full support if they decide not to compete.
Commonwealth Games Federation president Mike Fennell insists the event will go ahead as planned from 3 October, despite the problems.
Among those to withdraw are world champion discus thrower Dani Samuels from Australia, and Olympic 1500m champion Asbel Kiprop and 10,000m champion Linet Masai from Kenya, citing health and security concerns.
Athletes putting faith in NZOC
The New Zealand Athletes Federation says many athletes are waiting for assurances from the NZOC that they will be safe in Delhi.
The head of the federation, Rob Nichol, says the fact the Games Village and other facilities in Delhi are not finished yet is of less importance than questions over security.
Mr Nichol says police in Delhi are testing security plans this week under the scrutiny of international officials, including members of the NZOC, but some athletes may decide not to attend the Games.
Lawn bowls player Val Smith says she will feel safe if the NZOC give them the go-ahead, but says it is hard to concentrate on the task ahead with all the uncertainty.
The Delhi Games will be the first Commonwealth event for archer Steve Clifton, who says he is excited about competing in India.
Clifton says he has faith the security and facilities will be up-to-scratch by the time he arrives. He says his major concern is an outbreak of dengue fever.
Cancellation may spell 'permanent end' to Games
Commonwealth Games silver medalist Dick Quax says if this year's event in Delhi is cancelled, it could signal the end of the Games forever.
Mr Quax, a former distance runner who represented New Zealand, told Nine to Noon it would be devastating for the athletes if they could not attend.
He said that if the Games are cancelled, it would not only be embarrassing for India but could signal the end of the Commonwealth Games, as they are increasingly expensive to hold.