The Scottish Police Federation (SPF) has said a violent incident in Glasgow raised questions about whether officers can protect the public.
SPF chairwoman Andrea MacDonald said it was "deeply worrying" that no armed officers were dispatched.
The attacker in Thursday's incident injured two people before inflicting fatal injuries on himself.
Police Scotland has insisted that the incident did not require the presence of armed officers.
One of the victims of the attack was reported to be in a stable condition in hospital with injuries to his shoulder and arm.
The other victim, a community warden, was allowed home after treatment.
Ms MacDonald said: "Had the assailant been intent on harming large numbers of the public, he could have done so with impunity and the police would have been largely powerless to stop him.
"Whilst not detracting in any way from the courage of the police officers who attended, the fact no armed officers were dispatched to a man attacking others with knives and an axe should be deeply worrying.
"Glasgow is a city with an almost permanent armed police presence but they were not dispatched and they did not attend."
She added: "This lays bare the myth that the service adequately risk-assesses incidents prior to deploying resources and that as a service we are capable of protecting the public from spontaneous incidents of extreme violence."
The SPF annual conference - last month - heard calls for all officers to carry Tasers and for there to be an increase in the number of armed officers.
Police Scotland has rejected these calls and stressed the value of retaining a largely unarmed police service.
Assistant Chief Constable Wayne Mawson said: "Police Scotland, along with the rest of the UK, prides itself in being an unarmed service with access to specialist firearms support whenever required.
"Yesterday's incident in Glasgow city centre was a dynamic and fast-moving incident. Local officers responded rapidly and contained and dealt with it quickly.
"This was not a random attack. It was planned and targeted, and armed officers were not required to attend on this occasion."
Detectives have appealed for information about what they said was a "targeted" and pre-planned attack.
The incident has been referred to the Police Investigations and Review Commissioner (PIRC).