The tests will be available through pharmacies within the next two weeks.
Following the meeting the prime minister told reporters in Canberra 200 million rapid tests would be coming to Australia over the next two months.
Following widespread shortages of the rapid tests and large queues at PCR testing clinics across the country, the prime minister announced changes to testing requirements to alleviate pressure on the system.
People who return a positive COVID result from a rapid antigen test no longer need to have their infection confirmed with a PCR test.
Testing sites will also begin administering rapid tests to help ease the pressure on pathology labs.
Mr Morrison said universal access to free rapid tests was not agreed to by any state or territory leaders or the federal government.
"The cost for those tests being provided concessionally will be met 50-50 by the states and territories and the Commonwealth," he said.
However, Opposition Leader Anthony Albanese has called on the government to make the tests free for everyone, labelling the Commonwealth's plan as a failure.
"It's very clear the simplest way to do it is to make tests free and make them available," he told reporters in Sydney.
"People are crying out for action, the economic consequences of this government's failure to put in place a proper system are there for all to see."
Mr Albanese had previously called for the rapid tests to be made affordable but has since changed to wanting tests to be free.
"We've considered the options and the clear and simplest, most cost-efficient way is to make tests available," he said.
Rapid tests have been made free in countries such as the US, UK and Singapore.
The Public Health Association of Australia and Australian Medical Association have also added their voices to the chorus for free rapid tests.
Mr Morrison said Omicron had caused a major disruption in Australia, and that making the rapid tests free for all would not immediately solve issues.
"There's no silver bullet, making everything free is not a silver bullet," he said.
"You've just got to work the problem, work it together and push through, and that's what we'll be doing at national cabinet."
National cabinet was also due to consider whether to change the criteria for who is included in hospitalisation figures.
The discussion comes after it was revealed earlier in the week that some people were being admitted to hospital for non-virus related health issues before later testing positive.
On Tuesday, there were 176,223 boosters administered across the country, the highest daily number for the third doses.
More than 64,000 COVID cases were reported nationally on Wednesday, the highest daily number since the pandemic began.
NSW registered a high of 35,054 cases and eight deaths, while there 17,636 cases and another 11 deaths in Victoria.
Tasmania had a record of 867 infections, with Queensland reaching 6781, SA with 3493, the ACT with 810, NT 117 and WA 16.
