The Pfizer vaccine will be administered by some 500 GPs across Australia today, for the 40 to 59-year-old age group.

Victoria is already claiming that its Pfizer allocation is dwindling, while NSW gets more to battle its unfolding virus outbreak.

Deputy Chief Medical Officer Michael Kidd says a further 800 GPs will come on board during July and August, including many Aboriginal community-controlled organisations.

However, there is no exact timetable provided for under-40s Pfizer vaccination.