Doctors and other experts have warned the target will not be met after logistical issues and minor bungles put the jabs behind schedule.
More than 86,000 people had received their first injection as of Sunday, which marked the second week of the rollout.
While the program was always designed to ramp up as it progressed, the government now needs to dramatically increase administration to reach its goal.
Morrison said he remained confident all Australians who wanted a vaccine would have access to one by the end of October.
“That doesn’t mean we won’t hit some obstacles,” he told reporters in Sydney on Tuesday.
“It doesn’t mean there won’t be the odd frustration, the odd logistics issue that needs to be addressed. That’s to be expected with a project of this scale.”
The prime minister expects the figure to break 100,000 this week, fuelled by supplies of overseas-produced vaccine.
Later in the month, doses of the AstraZeneca jab produced in Melbourne are expected to be added to the network at a rate of about one million a week.
Morrison said early issues had been resolved as he declared total confidence in the vaccination program led by medical experts.
“It’s a strategy that was pulled together last year and has been meticulously worked through even now as we roll the vaccines out,” he said.
The head of the prime minister’s department will on Tuesday front the Senate’s coronavirus response committee.
Phil Gaetjens is expected to face questions about his efforts to better co-ordinate restrictions between states.
He is working with his state and territory counterparts on analysing changing risk profiles as vaccinations boost Australia efforts to remain on top of coronavirus.
The government is also taking steps to ensure communications are targeted to Aboriginal and Torres Strait Islander people, who have an increased risk of serious disease.
Coronavirus vaccines will start arriving on the Torres Strait islands in coming days and Cape York joins the rollout soon after.
The islands closest to Papua New Guinea will receive the first vaccinations given the risk the disease could spread from Australia’s close neighbour.Jump to next article