Exclusion zones could be set up outside Victorian hospitals following anti-vaccination demonstrations at the weekend.
Premier Daniel Andrews said his government will look at any proposals about how the zones could work, but is not considering formal plans just yet.
"We will work with hospitals and our health unions to monitor that and to act on the very best advice," he told reporters at state parliament on Tuesday.
Mr Andrews described the behaviour of about 200 activists outside the Royal Children's Hospital, Royal Women's Hospital and Royal Melbourne hospital on Saturday as "fundamentally wrong".
Police stood guard at an entrance to the pediatric hospital, escorting some families through the area so they could avoid the chaos.
Safe access zones are currently in place around Victorian abortion clinics, banning protesters from getting within 150 metres, blocking nearby footpaths or harassing patients.
Federal Labor MP Rob Mitchell has written to Victorian Attorney-General Jaclyn Symes pushing for a 250-metre exclusion zone, after being contacted by constituents with family members in the Royal Children's Hospital.
"People just felt very uncomfortable about it, they've got sick kids," he told AAP.
"We need to have a look at this before it gets out of control ... we should have our right to protest absolutely, but it needs to be appropriate."
Ms Symes confirmed she is considering whether hospitals need greater protections similar to those already in place for abortion clinics.
"It's something that I'm keen to have a look at," she said.
"The public outcry would send a strong message to (the protesters) that this is not an appropriate way to voice your concerns.
"People are trying to visit their sick kid. Come on, you can choose more appropriate environments (to make a protest)".
The Victorian opposition does not believe hospital exclusion zones would be the most effective way to deter similar protests.
Opposition Leader Matthew Guy wants a return of "move on" order provisions scrapped by the Andrews government in 2015.
"Those move on laws would have cleared off those fools from the front of the children's hospital and it would have been able to give police the ability to charge them should they need to," he said.
