Condemning the incident, Vijayan said the government would take strong steps against those behind the attack on the mayor.
"RSS workers, accused in several cases entered the visitors' gallery. In the well-planned attack carried out without any provocation, BJP councilors also joined in. RSS took the lead in the attack," the chief minister said.
Vijayan said he was informed by doctors treating the mayor that the latter had suffered serious injuries on the back of his neck.
If the attack had been a bit more severe, the mayor's backbone would have been injured, leaving him paralysed, the Left leader said.
He also said that a section of media had reported the incident as a minor scuffle, which was "not right".
The incident was unfortunate and strong action would be taken against those behind the attack, Vijayan said, adding BJP women councilors attacked LDF women councilors.
CPI(M) state secretary Kodiyeri Balakrishnan also hit out at the RSS/BJP over the incident.
Congress leader V M Sudheeran and CPI state secretary Kanam Rajendran were among those who visited the injured mayor and enquired about his health.
Police said two cases have been registered against the BJP and CPI(M) councilors.