Brisbane man John Preston, 58, had pleaded not guilty to two counts of failing to comply with the directions of a police officer over the March incidents.

The prosecution told Magistrate Catherine Rheinberger that the inspector overseeing the case decided two days ago not to pursue the charges, and would tender no evidence against Mr Preston.

Mr Preston was charged with refusing to move on from the areas at the request of police, who acted based on the belief he may commit an offence.

Police suspected it was likely he may commit an offence under the new Reproductive Health Act, which restricts protests from taking place within 150 metres of a pregnancy termination clinic.

Prosecution lawyers said today on review of the legislation, it was determined Mr Preston wasn't likely to commit an offence. 

Mr Preston addressed media outside the Hobart Magistrates Court and said every child had a right to life.

''It's pretty incredible two days before the hearing they decide to pull out,'' Mr Preston said.

''Does it mean it is perfectly alright to hold up pictures like this in public everywhere in Tasmania?''