Council staff spent Monday removing messages around city entry points, with mayor Dean Rees saying these actions only hurt the community.

The abuse included calls to sack or hang Mr Andrews, honk if drivers hated the Premier and also labelled him a cross-dresser.

"I understand the frustration of a person who's sick of these lockdowns, hurting businesses etc. but I think there's another way to vent your frustration and anxiety over it," Cr Rees said on Tuesday.

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"We've had our guys out yesterday removing the signage, which costs time and effort and labour on times when they're not supposed to be out and about but we didn't want that as an entrance into our city.

"Please don't deface council property because it's you, the ratepayer who eventually ends up paying for the removal of these signs and all us ratepayers."

Cr Rees condemned the nature of the messages

"It's almost a death threat," he said.

"That's what incited the violence in America and we don't want it inciting violence here in our community with hatred like that."

He said petitions would be more appropriate than graffiti if people disagreed with the government's actions.

"To threaten somebody's life is not the right attitude to take in this situation, in any situation," the mayor said.

"(Mr Andrews) is doing what he believes is right. Inciting violence isn't the right way to go."

Cr Rees advised people instead to contact the council with their concerns, which could then be passed on to the state and federal governments.

People began sending him photos of the vandalism on Saturday morning, suggesting it was carried out around the time the five-day Victorian lockdown began late Friday night.

Several messages used the same spray paint, possibly indicating a single culprit.

Cr Rees hoped the lockdown would end after five days and restrictions ease in regional Victoria.