A division bench comprising Justices A. Selvam and N Authinathan gave the direction when a habeas corpus petition by Thenmozhi came up for hearing.
Public Prosecutor (PP) Rajarathinam informed the bench that Murugan, who was observing a "fast unto death" from August 18, had ended it yesterday.
The bench had earlier sought Murugan's medical reports which were submitted by prison authorities.
As Murugan was only consuming water from the day of his fast, authorities recommended that he be shifted to Vellore Government General Hospital for treatment.
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On Thenmozhi's plea for meeting Murugan, the bench asked the PP about allowing her to meet him.
The PP then submitted that if a fresh representation was made by her, prison authorities would consider and pass orders on the application as per the prison manual.
Recording the submission, the bench directed Thenmozhi to make a fresh application and directed the prison authorities to pass orders within three days.
The court had yesterday asked the Additional Public Prosecutor why permission has been refused to visitors to meet the convict, to which the APP submitted that as per the prison manual, if any inmate goes on a fast, no one is allowed to meet him and all facilities made available to him are cut.
Citing various news reports about Murugan's fast, she had said it was the duty of the prison authorities to save his life.
She had said Murugan was in the prison for the last 26 years.
The officials had rejected her August 22 representation to meet Murugan, she said and claimed that even his wife Nalini, a co-convict in the case, was also not allowed to meet him.
The Supreme Court had in 2014 commuted his sentence and of two others to life imprisonment citing the delay in deciding their mercy plea.
Nalini is also serving a life term after her death sentence was commuted by the state government.