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Premier Daniel Andrews has confirmed the border will close at 11:59pm on Tuesday following crisis talks with NSW Premier Gladys Berejiklian and Prime Minister Scott Morrison.
"We have, all of us, agreed that the best thing to do is to close the border," Mr Andrews told reporters on Monday.
"That closure will be enforced on the NSW side so as not to be a drain on resources that are very much focused on fighting the virus right now across our state."
A permit system for travel between the states will be outlined by Ms Berejiklian later on Monday.
There will be specific arrangements put in place for people in border towns such as Albury-Wodonga to carry out daily activities or receive healthcare.
Mr Andrews said the border closure means staff at airports and train stations can be redeployed into "much more important roles".
He said stood-down Qantas staff have been called up to work in the hotel quarantine program in Victoria, reporting directly to the Department of Justice.
More than 100 additional personnel from the Australian Defence Force will also be called in to help.
Thirty-four of the new Victorian cases are linked to confirmed and contained outbreaks, 40 were discovered through routine testing and 53 cases are being investigated.
Chief Health Officer Sutton Brett Sutton said the number of known cases in the nine locked-down public housing towers at Flemington and North Melbourne has almost doubled since yesterday, from 27 to 53.
Sixteen of Monday's cases are residents in the towers, while a further 10 cases from previous days have now been linked to the buildings.
"So it's an increase of 26, essentially doubling of the numbers from yesterday and really not unexpected," he said.
"It is exactly the reason why these towers are in a hard lockdown and why we're doing extensive testing across all of them."
More than 3000 meals and 500 hampers of food were distributed to residents in the towers on Sunday, while about 350 personal care packs, including soap, deodorant, toothpaste, nappies and baby formula have been handed out on Monday morning, as well as bread and milk.
Professor Sutton said levels of community transmission are at "reasonably low" levels, with 13 new infections linked to community transmission today.
Increases of 20-30 community transmission cases per day were recorded last week.
Meanwhile, a man in his 90s has succumbed to the virus in hospital, becoming the 21st person to die from the virus in the state. His death also brings the national toll to 105.
The previous daily high for the number of new COVID-19 cases recorded in Victoria was 111 on March 28.
Mr Andrews said the rising number of new cases is "challenging".
"All of us have got a part to play in getting control of this virus, stabilising it, driving down case numbers, containing it and then getting back to a point where we can resume our program of opening up," he said.
"This could not be more serious."