Warrnambool Sergeant Martin Flannery said regular patrols were being conducted by all police units across the city.

"We urge people not to gather in groups and stay home, particularly those who have travelled overseas," Sergeant Flannery said.

"We have patrols dedicated to checking addresses where people are supposed to be isolating.

"Patrols have also been engaging with members of the community and businesses advising them on how they should behave in these circumstances and that people adhere to self-isolation instructions."

He said all police units were undertaking COVID-19 operations, including the highway patrol unit, divisional tasking team and crime scene operatives.

Returned travellers and businesses face steep fines in Victoria for breaching quarantine and mass gathering rules as the states coronavirus cases jumped by a record number to almost 700.

The total confirmed virus cases in Victoria spiked by 111 to 685 on Saturday, the state's biggest single day jump of the COVID-19 outbreak.

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It comes as the government announced tough new on-the-spot fines of $1652 for travellers found to be out-and-about within 14 days of returning from overseas.

Businesses breaching restrictions about mass gatherings - including weddings, funerals and auctions - face penalties of up to $9913.

Premier Daniel Andrews told people to stay home to stop the spread of coronavirus, despite clear skies and warm weather over the weekend.

He foreshadowed tighter stage three restrictions but did not say what they involved or when they would come into effect.

"(It's a) beautiful day today. Sadly, you need to stay home," Mr Andrews told reporters on Saturday.

Warrnambool City Council mayor Tony Herbert welcomed the tough new measures but acknowledged the impact on the community, particularly on businesses.

"We'll abide by anything the state government says," he said.

"It's really tough, it's heartbreaking to see businesses shutting down and I just feel so sad for them.

"Warrnambool was just on the cusp of something, we had the livability accolade and we had such a diverse range of restaurants and cafes.

"It's really hard but it's about what we can all do to keep ourselves safe, we will get through it. We're a tough little community and we're all looking after each other."

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