Swiss police have issued an international arrest warrant after a man went on the rampage with a chainsaw in the town of Schaffhausen.
Suspect Franz Wrousis, 50, is still on the run more than 24 hours after the attack on a local health insurance office close to the German border.
Five people were hurt. The victim with the most serious wounds is now out of danger, police said.
They believe the suspect is still armed with the chainsaw.
Police released a new photo of Franz Wrousis on Tuesday and said he had convictions for weapons offences in 2014 and 2016. "Anyone who sees him should avoid him," a spokesman warned.
They said he had been wearing the same green jacket shown in the picture and that he was carrying three bags, including a black bin-type bag thought to contain the chainsaw.
Police with dogs spent the night searching an area close to the German border.
However, officials in the German state of Baden-Württemberg said there was no evidence that the suspect had left Switzerland.
The suspect was said to have lived in local forests close to the border for some time, and photos issued by police on Monday showed a man of dishevelled appearance.
The attack unfolded shortly after 10:30 (08:30 GMT) on Monday, when two workers were attacked and wounded by a chainsaw at the CSS insurance office. One was badly hurt and needed surgery in hospital.
Police said Franz Wrousis had been a customer of the agency.
Two customers suffered shock and a bystander was slightly hurt during the ensuing security operation, police said.
The suspect's vehicle was found on Monday and prosecutors warned he was "aggressive and dangerous".
As the manhunt continued on Tuesday, all the insurance agency's offices were shut in the immediate area and children's holiday activities were cancelled.