Victoria’s cluster of cases has reached 15, with authorities naming dozens of exposure sites including the MCG where an infected person attended an AFL match on Sunday.

Liberal senator Jane Hume is concerned three Victorians at the centre of the outbreak were not vaccinated despite being eligible.

“The most important thing for Victorians is that they get out and get themselves vaccinated,” she told reporters in Canberra on Wednesday.

“We heard that of the new cases that were announced overnight and yesterday as well, three of them were over 50 that could have been vaccinated, so that increases the urgency to get the vaccinations done.”

The outbreak in Melbourne has raised questions about hotel quarantine and the speed of the vaccine rollout.

Home Affairs Minister Karen Andrews denied federal government supplies were hampering the rollout despite Australia lagging well behind other nations.

“There are adequate supplies at this point so please go out and get vaccinated,” she told Sky News.

Labor argues the prime minister could be doing more to keep Australians safe.

The Melbourne outbreak is linked to a man who fell ill earlier this month after completing hotel quarantine in Adelaide.

Labor health spokesman Mark Butler said the federal government should be moving faster to fund state proposals for purpose-built quarantine facilities in Victoria and Queensland.

“We need to speed up the vaccine rollout but we also need a safe national quarantine system” he told the ABC.

“We can’t continue to see these outbreaks from a quarantine system based around hotels, which were built for tourism, not medical quarantine.

“We don’t have national standards still in our hotels around ventilation, around the use of personal protective equipment. We still have staff in our hotels doing quarantine who haven’t been fully vaccinated.”

Ms Andrews said the Commonwealth was doing its own due diligence on the Victorian quarantine proposal but could not put a timeline on when a decision would be made.

“This is a very important proposal that has been put forward. It is a comprehensive proposal, which is excellent – that’s what we need.”

Labor is also urging the government to redraft vaccination plans and scrap its tiered program for getting a jab.

Just under 3.7 million doses of coronavirus vaccine have been administered across the country, well short of initial targets.

State and territory governments have defied the staggered approach to the vaccine rollout and opened eligibility to new groups ahead of the federal government.

New restrictions have been imposed across Melbourne, including mandatory mask-wearing indoors and limits on gatherings, but the state government has so far resisted a lockdown.

States and territories have tightened borders with Victoria but stopped short of complete closures.