There were 42 people who returned a positive result and more than 30 people who were identified as a close contact.
The ABC reports that since then, several of those would-be passengers had sought another test after experiencing no symptoms.
The subsequent testing reportedly returned negative results.
A spokeswoman for Qantas told 9News that the company was investigating the accuracy of the tests, and whether the pathology company assigned to conduct them had outsourced work.
“I can confirm that is something that we’re reviewing,” the spokeswoman said.
“We have reiterated to our diagnostic agency that they must ensure that any laboratory they use has all current and appropriate accreditations.
“We continue to work with DFAT to ensure the process is working as it should.”
The spokeswoman added that “all the protocols put in place were designed to minimise the risk of importing the virus” and maximise the safety of everyone on board.
Prime Minister Scott Morrison weighed in on the topic on Sunday afternoon, saying that he doesn’t think Australians are being “unfairly blocked”.
“We will work with Qantas who run the testing program for people getting on planes,” he said.
“But the testing has got to be up to standard.
“It’s a very difficult environment to operate in, where India is right now. We’ll work with Qantas, they’re conducting that testing regime… and they’ll get every support from us. But it’s a difficult environment at the moment.
“When it comes to protecting Australians health and safety here, then we’re going to be cautious, I know what side of the line we need to be cautious on.”
Those who missed their original flight from India earlier in the week are believed to now be in a ‘high-priority’ group and will soon be flown back to Australia, however, it is unclear if they will be on board the next scheduled repatriation flight on May 23.