The hard lockdown for residents in Melbourne's nine public housing towers will be eased as soon as testing is completed.
They will then revert to the provisions of the new six-week lockdown announced on Tuesday for the rest of the city.
"There are teams going out floor by floor and door by door to do the important testing," Premier Daniel Andrews said.
"As soon as we can get the testing down, we'll be in a position to assess the data and make new rules for the towers."
The towers lockdown order is for 14 days, but Mr Andrews wants it to end in five.
It comes as authorities apologised for the delay in delivering donated food and supplies to the thousands of residents in the towers.
Donations were turned away from some of the towers in Flemington and North Melbourne on Monday night.
Residents are into day three of the hard lockdown, which was ordered after a spike in cases there, with 69 confirmed by Tuesday.
They spent the first two days relying on deliveries of food and supplies from the state government, some of which was expired, insufficient or culturally inappropriate, such as pork being provided to Muslim families.
The Melbourne Public Tenants Association said residents had been left in the dark since the lockdown was enforced on Saturday.
In a letter to the federal acting chief medical officer, the DHHS, Mr Andrews and Victoria Police, the association described the government-provided food during the first two days as "at best, questionable pre-packaged meat-like food items that do not look suitable for human consumption.
"Furthermore, the delivery of the food was tossed to the floor on a single piece of paper in front of the residents' apartment doors in small portions of one food item per household."
Voices from the Blocks, a coalition of residents and community members, said they were horrified to see donated items being confiscated by authorities.
"(We) watched in horror last night as food, medicine, and essentials like nappies and baby formula were suddenly confiscated by authorised officers," the group said on Tuesday.
The Department of Health and Human Services acknowledged there were "some delays with accepting donations and deliveries, which caused confusion at some housing estates that are in lockdown".
"We apologise for the inconvenience and frustration caused and thank the residents for their co-operation and patience."
The donations have since been returned to the towers.
Abdiraham Ibrahim, a father of five living in a Flemington tower, said supplies were more accessible on Tuesday.
He had earlier been forced to rely on friends to deliver necessities, such as milk and baby formula.
"If the government are not providing what we need, they shouldn't be stopping people from bringing it," he told AAP.
Mr Ibrahim said bags of groceries had been left in the foyer of his apartment block but he was concerned some people may not know they had to go downstairs to get it.
"Our neighbour is 65 years old and doesn't speak English. She doesn't know," he said.
Mr Ibrahim was also worried the bags could spread the virus.
"People are touching this bag and that bag, what if they have the virus?" he said.
Opposition spokesman for housing Tim Smith urged the government to outline its plans to stop the spread of the virus in the towers.
"The 3000 residents of the towers in Flemington and North Melbourne who are virtually under house arrest are paying for Daniel Andrews catastrophically poor leadership," he said in a statement.