About 80 returnees are now in quarantine in the Howard Springs facility in the Northern Territory after they landed from India on Saturday following the lifting of the travel ban from the virus-ravaged country.
The plane was only half full because more than 40 people who tested positive pre-flight along with about 30 of their close contacts were barred from returning.
However, there are reports of some inconsistency in the testing results, adding to the frustration of Australians wanting to return home.
The prime minister conceded India is a very difficult environment to operate in right now.
"We will work closely with Qantas who are obviously conducting that testing regime as part of their process and they will get every support from us," Mr Morrison told reporters in Gladstone, Queensland on Sunday.
"I hope and intend for us to get even more home in the other repatriation commercially facilitated flights in the weeks ahead."
But he said it was essential to have a rigourous testing regime when coming to Australia, whether it is India or other countries like the UK.
"I have seen the suggestions from others who seem to think that we can put people who have tested Covid positive on planes and bring them into Australia," he said
"I mean that just doesn't make any sense."
Even so, Opposition leader Anthony Albanese said Australians in India are very frustrated and while they are there, they are exposed to real health concerns.
He said if Australians had been brought home by last Christmas as the government had promised, they wouldn't be Covid positive now.
"If Scott Morrison had of kept his commitment, they wouldn't be exposed to this danger," he told reporters in Narangba, Queensland.
"If the federal government had have listened to (Queensland) Premier Palaszczuk last October the quarantine centres that she proposed, appropriate facilities, would be built now, would be opened, would be able to be used."
More than 9000 Australians are registered as wanting to return, with about 900 of them said to be desperate or vulnerable.
The next government-facilitated flight is expected into Darwin on May 23, bringing up a total of 40 such flights since March 2020.
Meanwhile, coronavirus-related restrictions across Greater Sydney will ease from midnight on Sunday after NSW recorded another day of zero locally-acquired Covid-19 cases.
It means mask usage will not be compulsory on public transport and the limit on private gatherings in home will lift, restrictions that were imposed 10 days ago after a mystery east Sydney case was reported.
