Thousands of long awaited Pfizer-BioNTech vaccines against COVID-19 arrived across Asia Pacific at the weekend in what one regional leader called "the biggest ever peacetime logistical operation."

Australia began coronavirus vaccination efforts on Monday while Malaysia has moved its rollout up by two days to Wednesday.

Australian Prime Minister Scott Morrison received his first dose on Sunday, but most citizens had to wait until Monday to roll up their sleeves for a jab.

Roughly 60,000 doses are to be given this week in the national capital of Canberra, 22-year old nurse Maddy Williams was the first to be inoculated.

Front line healthcare workers and the elderly take precedence at the moment, and authorities hope to have 4 million Australians vaccinated by the end of March.

"We have been eagerly anticipating this day since the vaccine first received approval [...]We are about to embark on our state's biggest ever peacetime logistical operation," said South Australian Health Minister Stephen Wade.

Malaysia received 312,290 doses of Pfizer the vaccine on Sunday, two days ahead of schedule, with more shipments planned in the coming weeks.

More than 500,000 Malaysian frontline workers will be the first to be inoculated between now and April, Prime Minister Muhyiddin Yassin said, followed by nearly 10 million high-risk individuals.

Pending regulatory approval, shipments of China's Sinovac vaccine are also expected to begin arriving later this week in Malaysia, according to Science Minister Khairy Jamaluddin.

While countries across Asia Pacific are welcoming vaccine deliveries this week, in Japan waiting times are growing longer.

The country's inoculation chief announced on Monday that only limited doses of COVID-19 vaccines will be available for the first month, meaning the elderly will receive their jabs more gradually than predicted.

Japanese health authorities have only approved the Pfizer vaccine and 144 million doses are now expected to arrive in May.