Lukas Duczko has revealed to the Expressen daily that he was told by the operator at Sweden's emergency response service, SOS Alarm, that no confirmation could be given and that they were very busy at the time.
"I had been talking for seven minutes and saw how Anders was shaking. Then I said that she has to ensure that an ambulance be sent immediately. Then she told me to calm down," he told the newspaper.
Another member of the party then put in a call to the 112 emergency line and was given the prompt response that an ambulance was on its way.
In a statement on Monday, SOS Alarm denied that the Wallner had been obliged to wait unduly long for an ambulance.
"The ambulance was at the location 17 minutes after the first call came in," said SOS Alarm press spokesperson Anders Klarström.
The knife attack reportedly occurred shortly after midnight. According to police, Wallner managed to proceed to the Skärholmen metro station where he was found seriously wounded.
Wallner was rushed to Stockholm South General Hospital (Södersjukhuset) and underwent an operation during the night.
Anders Wallner, who is in the running to become the Greens new party secretary, communicated via his Twitter account on Monday that he "feeling well under the circumstances".
Anders Klarström told The Local earlier on Monday that SOS Alarm had opened an internal investigation into the incident.
"The inquiry showed that all routines have been followed," the firm later confirmed.
Anders Wallner's friends have however filed a police report against SOS Alarm, which came under fire in a separate case recently after it emerged that a 23-year-old Stockholm man had died after having been refused an ambulance.
Emil Linnell made several calls to SOS Alarm late on January 30th complaining of breathing trouble, but the on-call nurse deemed his condition not to be life-threatening.
The transcript of the communication between the nurse and the man, released in April, shows that he pleaded "help me" repeatedly on the phone to SOS Alarm but was ignored.
Several hours later the 23-year-old was found dead by a neighbour; the cause of death was a ruptured spleen. No ambulance was ever sent.