An abortion clinic in East Melbourne is asking the Supreme Court to order Melbourne City Council to deal with people it says are harassing female patients and staff.

Law firm Maurice Blackburn said a group calling itself Helpers of God's Precious Infants stand outside the Fertility Control Clinic trying to stop women getting abortions.

Lawyer Lizzie O'Shea said the clinic was a ratepayer and resident of the city council and had the right to be protected.

"They're bringing an action which alleges that the Melbourne City Council has failed to act upon a duty that it has under the Public Health and Well-Being Act," she said.

"That duty is to remedy nuisances occurring in its municipal district that are dangerous to health."

In July 2001, security guard Steve Rogers was fatally shot at the clinic.

Anti-abortionist Peter James Knight was convicted of his murder and is serving a life sentence with a non-parole period of 23 years.

"[Steve Rogers] was shot and killed working at the clinic by a person who was standing with the people out the front of the clinic, even though they say he had nothing to do with them," Ms O'Shea said.

Melbourne Lord Mayor Robert Doyle called the protests outside the clinic "shameful", but said those involved still had rights.

"I've got a great deal of sympathy for those young women who are harassed in, I think, quite a vile way, as they enter that clinic," Cr Doyle said.

"At a difficult and sensitive time in their lives they don't need a bunch of idiots giving them a hard time.

"Despite the fact I don't like the protest at all, and I don't think they've conducted themselves in any honourable way, they do still have rights as protesters.

"It's a pretty delicate balancing act and we'll continue to work with Government and with the clinic.

"People have a right to protest but they don't have a right to impinge on other people's rights, and that's unfortunately what has happened at that clinic from time to time."

Cr Doyle said he did not support the idea to put up barriers around the clinic to separate protesters from patients.

"I wouldn't like to see barriers in our city, I don't think that's the way we want to conduct ourselves," he said.

"When there are complaints we can have compliance officers go down there, but in truth it's a very difficult situation."

The ABC has contacted the Helpers of God's Precious Infants for comment.

Clinic 'disappointed' in council's response to protesters

Ms O'Shea said the Fertility Control Clinic had been complaining to the council for a number of years.

"Unfortunately those complaints have been rejected by the Melbourne City Council, so we think it's important to clarify in law what their duties are," she said.

"And to make sure that if they've got a duty, which we say they do in this incidence, then they're required to act upon it and not just turn a blind eye to the really significant harassment that goes on."

Ms O'Shea said this was the latest action in a long list of attempts over a number of decades from the abortion clinic to solve the problem.

"They've liaised with police in the past, obviously Melbourne City Council and various members of Parliament, and they've now had to resort to litigation, I think with a heavy heart," she said.

"We'd prefer not to be litigating, that's for sure, but we feel disappointed Melbourne City Council hasn't done what we think they're required to do at law to deal with this problem."

Ms O'Shea said the people standing outside the clinic considered themselves to be "sidewalk counsellors" rather than protestors.

"They consider themselves to be on the frontline trying to stop women from getting abortions," she said.

"Abortion is a lawful health treatment that is provided for in Victorian law, and I don't think it's good enough that we just allow people to create emotional and physical barriers to people accessing that treatment because they object to it.

"The proper place for them to voice their views is with lawmakers if they want to seek reform."

Women intimidated by protesters: psychologist

The civil trial is hearing from eight witnesses, including Dr Susie Allanson, who has been the centre's clinical psychologist for 24 years.

Outside court, Dr Allanson said the protestors had been there ever since she started working at the clinic.

Dr Allanson said anti-abortion protesters can intimidate women into not returning for important follow-up appointments. ( ABC News: Peta Carlyon )

She said she was aware of instances where patients were so intimidated they delayed returning for important follow-up care.

"Protestors can follow women, try and walk beside them and give them pamphlets that are anti-abortion, anti-contraception," Dr Allanson said.

"They can say things like you're a mother now, don't kill your baby, you'll need counselling after this, it will cause cancer, your relationship can break down.

"They will go up to cars and they will make it so that people struggle to get out of their car.

"At times I've seen them when there are children in the car as well... I think that's appalling."

Dr Allanson said at times, the confrontations had escalated.

"It's very difficult for people where you have a complete stranger getting into your face and space," she said.

"I find it very difficult myself. Usually I try and ignore them, but usually if I have an encounter with one of them I'm pretty shaky afterwards, it takes me a while to come down.

"You're constantly having a bit of a stress reaction... if I venture out I won't go out unless there is a security guard there."