Asked repeatedly on Friday if he would support the probe, Mr Morrison instead pointed to the now-concluded Senate parliamentary committee.
"Our (federal government) experts have been available to that inquiry each and every time," Mr Morrison said.
Last month, that Senate committee on COVID-19 called for a royal commission into the government's pandemic response.
"We think the government's response has been characterised by a failure to be prepared, a failure to take responsibility, and then a failure to get it right," chair and Labor senator Katy Gallagher said in April.
Labor leader Anthony Albanese on Friday backed calls for an inquiry.
"I cannot envisage a situation in which whoever wins government wouldn't want to examine the once in a century pandemic and the response," Mr Albanese said.
"We have to examine it so that we learn the lessons."
While Mr Albanese said it shouldn't be a "political exercise" it would at times become political as it set its sights on the Morrison government's response.
Mr Morrison on Friday said the pandemic was still going, with new variants of the virus continuing to emerge.
It comes as the World Health Organisation says the real death toll from COVID-19 is nearly 15 million people, more than double the official figures.
The official death toll is just more than six million but the new estimate factors in people killed by the virus or due to the impacts of overloaded health systems.
Scientists reached the new 14.9 million total by factoring in uncounted deaths and indirect fatalities such as cancer patients being unable to access health services.
Meanwhile, doctors are warning Western Australia has hit the peak of its outbreak of the Omicron variant.
The Australian Medical Association said people needed to remain vigilant for the virus as WA reported more than 10,000 cases on Thursday.
About one in three PCR tests are coming back positive and the remote Kimberley area is reporting three times more cases than other regions.
"This is what occurs when you reduce restrictions while the pandemic is in the plateau phase," the AMA's WA president Mark Duncan-Smith said on Saturday.
He urged the state government to boost testing to get a clearer picture of the virus in WA while saying people should still be wearing masks indoors.
The state, which has taken a heavier-handed approach to keeping out the virus during the pandemic than other states, eased restrictions late last month.
LATEST 24-HOUR COVID-19 DATA:
NSW: 10,995 new cases, seven deaths, 1499 in hospital with 54 in ICU
Victoria: 10,305 new cases, nine deaths, 502 in hospital with 31 in ICU
Queensland: 7040 new cases, 11 deaths, 463 in hospital with 15 in ICU
Tasmania: 1107 new cases, no deaths, 46 in hospital with two in ICU
Western Australia: 9328 new cases, no deaths, 282 in hospital with nine in ICU
ACT: 1053 new cases, one death, 66 in hospital with five in ICU
South Australia: 2874 new cases, one death, 221 in hospital with 10 in ICU
NT: 381 new cases, one death, 46 in hospital with none in ICU
37°C