Goswami's counsel Sanjog Parab on Friday told the court that since April 16 has been declared as a holiday by the high court, the petitions could be heard later.
The police had named Goswami and all owners, managers, and all persons associated with Republic TV or ARG media under the category of "suspects".
Goswami, the Republic TV Editor-in-Chief, and two others are accused of abetting the suicide of Alibaug-based interior designer Anvay Naik.
Dasgupta is accused of having misused his official position and conniving with ARG Outlier Media, the company which runs all Republic TV channels.
The bench will hear ARG's main prayers challenging the police's investigation and seeking the transfer of probe to the CBI or any other independent agency, on March 16 via physical hearing.
The IAF had carried out the air strike deep inside Pakistan on February 26, 2019 in the wake of killing of 40 CRPF personnel in Kashmir's Pulwama district.
Sawant and Waghmare raised another issue of Republic TV allegedly illegally using Doordarshan Prasar Bharati satellite frequency signals without paying the uplinking fees to reach millions of additional subscribers free in an illegal manner.
Dasgupta, a diabetic, was rushed to the hospital from the Taloja Central Prison in Navi Mumbai in the early hours of Saturday after his blood sugar levels went up on Friday midnight.
The bench also said the Supreme Court, high courts and lower courts must be alive to the misuse of criminal law by the state machinery.
A vacation bench of Justices D Y Chandrachud and Indira Banerjee, which ordered that the accused shall not try to meet any witness in the case, said their release should not be delayed
The top court expressed concern over state governments targeting some individuals on the basis of ideology and difference of opinion.
The Bombay High Court had on Monday refused to grant interim relief to Arnab Goswami and two others in connection with the case and directed him to approach a lower court to seek bail.
The HC noted that the petitioner (Goswami) has the remedy under law to approach the sessions court concerned and seek regular bail.
Goswami and two others - Feroze Shaikh and Nitish Sarda - were arrested by Alibaug police on November 4 in connection with the suicide of architect-interior designer.
The Raigad crime branch found Goswami was active on social media using somebody's mobile phone, despite his personal mobile phone having been seized by police.
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