Deputy Prime Minister Barnaby Joyce said the tests "are there", but Australia was experiencing the same problems shared around the world.
Joyce has downplayed allegations his government failed to buy up enough tests in mid-to-late last year when the tests first came on the market.
"We're giving our best endeavours to make sure that (a pensioner will need to wait for a rapid antigen test)," he said.
It comes as rapid antigen tests become a key cornerstone of the back-to-school plan in NSW and Victoria.
School students and staff will be asked to submit to twice weekly rapid antigen tests as part of "surveillance testing". The federal government will pick up half the cheque.
Treasurer Josh Frydenberg said symptomatic Australians would soon be able to find the kits at their local pharmacy, with 200 million kits on order.
"The good news is more are coming online," he said.
"Every country is going through supply chain pressures … But we've got the highest vaccination rates and the lowest mortality rates.
"We should focus (Rats) on the most vulnerable cohorts, and we should ensure there is access for those people who need it most – they are the symptomatic people as well as those who are designated close contacts."
Health Minister Greg Hunt said on the weekend that pressure would ease off Australian pharmacies in coming weeks, as tens of millions of tests come online.
"It's a global challenge, I think it's very important to acknowledge that," Hunt said.
Hunt is said to have spoken to the Pharmacy Guild of Australia on Sunday to ensure Rats could be provided.
President Trent Twomey said on the Today show that as of today, pharmacies around the country "don't have enough".
"There are 6000 community pharmacies in Australia, 804 went live this morning … That means the majority will not be going live," he said.
"It is going to be fixed … There is 13 million arriving between now and next Monday.
"But like everything with this pandemic, we're competing with it, we're competing with global supply chain shortages on rapid antigen tests.
"Our big plan is quite simple - have some patience with your local pharmacy.
Frydenberg said anyone who needs a rapid test "right now" can go and get one from a state clinic.