The indefinite protest by over 400 employees of the Sanjay Gandhi Hospital in Amethi against the suspension of its licence entered the sixth day on Sunday.
The Uttar Pradesh government's health department recently suspended the hospital's licence and put a halt on its out-patient department and emergency services after a probe into the death of the 22-year-old woman.
Former Union minister and BJP leader Sanjay Singh demanded that while the woman's family should get justice, the hospital must not be shut down.
The guilty doctors should be punished after a probe but the hospital should function, he said and added that he will write to Chief Minister Yogi Adityanath in this regard.
The hospital's licence was suspended on September 17.
The woman was admitted in the hospital for a minor operation but her condition deteriorated on September 14 and she was rushed to a private hospital in Lucknow. She died on September 16.
Her husband alleged that she died due to an overdose of anaesthesia at the Amethi hospital.
The chief of the Sanjay Gandhi Hospital Employees' Union, also named Sanjay Singh, said the agitation will continue till the hospital reopens.
BJP MP Varun Gandhi has also written to the state government, urging it to reconsider the decision to shut the hospital. The hospital is named after the Pilibhit MP's father.
Congress leader Sonia Gandhi is the chairperson of the Sanjay Gandhi Memorial Trust, which runs the Amethi hospital, while party leaders Rahul Gandhi and Priyanka Gandhi Vadra are its members.