The junior doctors also demanded she come to the NRS Medical College and Hospital - the epicentre of the protests.
Banerjee visited the state-run Seth Sukhlal Karnani Memorial (SSKM) Hospital around noon, as the protesting doctors continued to raise slogans, shouting "We want justice".
"The Chief Minister's words are laced with threats. The cease-work could have been controlled had she paid a visit here and given a patient hearing to our demands. We will carry on our movement as our demands haven't been fulfilled," one of the protesting doctors at NRS said.
Banerjee's harsh words resulted in the resumption of emergency services at the SSKM, where senior doctors took charge, but there was a hardening of posture on the part of the striking junior doctors, who lashed out at the Chief Minister for having called them "outsiders", "urban Naxals" , "CPI(M) cadre" and "BJP workers".
They held a general body meeting and decided to continue the strike.
With the strikers unrelenting, Banerjee urged senior doctors to run the hospitals "smoothly and peacefully".
"Please take care of all patients. The poor people are coming from all districts. I will be honoured and obliged if you all please take full care of the hospitals," Banerjee wrote to the senior doctors.
Meanwhile, the protesting doctors at the NRS alleged they were attacked by hoodlums in a bid to break the agitation. One intern was injured.
"The hooligans pelted stones and threw water bottles. It is a shame that an intern of another medical college who was here to show us support got injured," a doctor said.
A seven-member delegation of junior doctors met governor Keshri Nath Tripathi and apprised him of the prevailing unrest in various medical colleges in the state and requested his intervention.
Earlier in the day, Banerjee termed the continuation of cease-work by the doctors despite the action taken by the government and the police, as a "political conspiracy".
On the other hand, Union minister Babul Supriyo sympathised with the doctors, but advised them not to make the patients suffer.
"Whatever happened in #NRS is deplorable iamp; a strong protest is very valid but it's also true that making other patients, including small babies, suffer due for no fault of theirs is also not something u can really justify," Supriyo tweeted.
"Strong action will b taken against U Hon'ble CM of WB, by the people of Bengal! People r suffering bcoz of your sick egotistical mentality - no one is safe in WB till U iamp; ur dirty Vote-Bank politics prevail here. It's a shame u can't say a simple sorry 2 the injured Young Doctors," Supriyo said.
Interestingly, condemning the government's role in the NRS case, Urban Development Minister and Kolkata Mayor Firhad Hakim's daughter Shabba Hakim (also a doctor), wrote, "We have a right to peaceful protest. We have a right to safety at work. P.S. as a TMC supporter I am deeply ashamed at the inaction and the silence of our leader".
Banerjee reiterated her experience at SSKM hospital and expressed disgust over the role of other political parties.
"Today when I visited SSKM, I saw gatherings of outsiders of different political parties shouting slogans in hospital silence zones and stopping emergency services. Patient parties are crying and outdoor services are closed," she wrote on Facebook.
Meanwhile, the administration of Burdwan Medical College and Hospital opened the gates after Banerjee's ultimatum and resumed emergency services which were stopped after four junior doctors were injured as outsiders hurled stones during the protest on Wednesday.
However, the junior doctors of the hospital continued their sit-in protest.
The protests erupted at the state-run NRS Hospital on Tuesday morning bringing regular services to a standstill, after a junior doctor was allegedly beaten up by the kin of a 75-year-old patient who died there late on Monday night. The family members of the deceased patient alleged medical negligence.
An intern named Paribaha Mukherjee sustained a serious skull injury in the attack and was admitted in the intensive care unit of the Institute of Neurosciences.
With improvement in his condition, Mukherjee has been shifted to the general bed and will be released from the hospital within the next two days.