Premier Daniel Andrews has flagged the possibility of beefing up roadblocks to stem any increase in non-essential movement between Melbourne and regional areas.
The focus on the checkpoints comes as regional Victoria looks set to move ahead of metropolitan areas in easing of lockdowns and police encounter trouble at some freeways posts outside Melbourne.
On Sunday the premier again highlighted Victoria's two weeks of low infection rates have prompted indicating the possibility that regional Victoria could jump two steps out of lockdown by mid-next week.
The step three changes would mean outdoor dining at cafes and pubs and up to five visitors in the home.
Victoria has reported 41 new cases of COVID-19 and seven further deaths, with the latest figures supporting the state's planned easing of lockdown restrictions.
Regional Victoria has record no new cases of COVID-19 and the rolling 14 day average, a key trigger for easing lockdown, dropped further below the threshold of five to 4.1.
Sunday's statistics for the past 24 hours take the state's death toll to 723 and the national count to 810 since the start of the pandemic.
As parts of Victoria move towards eased restrictions, some tensions are emerging, including reports of further protest action on Sunday and a dramatic vehicle stop north of Melbourne.
The premier on Sunday flagged further strengthening of the roadblocks to ensure the difference in restrictions would not lead to a flood of Melburnians trying to escape metropolitan restrictions.
"It may go to a new level to make sure that only those who absolutely need to be travelling into country Victoria are doing that," he said.
"If you don't have a a lawful reason to be travelling to regional Victoria, then you will be turned around and fined."
Mr Andrews said Melbourne should look to regional Victoria for the model in how to control the virus and be able to lift the restrictions but he said the good news around Step Three for regional Victoria flagged for this week needed to be accompanied by caution.
"This is proof positive that this is not theoretical, that this strategy is working, .... a slow and steady reopening and to stay open," he said.
"That sense of vigilance ( in regional Victoria) that has made this possible will still need to be there."
In one roadblock incident on Saturday a woman is seen being removed from the driver's seat of a car by a police officer in footage shared on Facebook on Saturday.
A masked Natalie Bonett refused to get out of her car after a discussion with an officer about a phone charger at Wallan, about 60km north of the city.
The male officer can be heard asking for Ms Bonnett's name and address.
"The problem is you're not stating your name to me," the officer is heard saying.
Ms Bonett again refused to get out of the car.
"I don't feel safe. You're armed," she said.
"You're safe, don't you worry about that," the officer replied.
The footage then shows the officer lean into the vehicle as Ms Bonett protests, before she is forcibly removed.
Police said the woman was asked for her name and address, but she refused to supply her details which is an offence under Section 59 of the Road Safety Act. When asked to produce her driver's licence, the woman also refused, which is also an offence under Section 59 of the Road Safety Act.
The woman was warned that if she did not provide her details, she would be arrested.
She still refused and was asked by police to get out of her car. When she refused this request, she was taken from the car by officers and taken into custody.
The Wallan woman was later released and is expected to be charged on summons with driving with obscured vision, fail to produce licence, fail to state her name and address, resist arrest, assault police and offensive language.
Melburnians are also set to receive some relief from Monday, with the reduction in hours of the daily curfew, to 9pm to 5am and the allowance of 'household bubbles', providing company for those who live alone.
Small anti-lockdown protests were staged in Melbourne on Saturday.
Police have arrested one person as anti-lockdown protesters massed at Melbourne's Queen Victoria Market.
Sunday's protest follows ones on Saturday when about 100 people demonstrated against strict Melbourne coronavirus restrictions across various locations.Police arrested 14 people and fined at least 50 for breaching health directions on Saturday.