A bench of Chief Justice Rajendra Menon and Justice A J Bhambhani issued notice to the Delhi government and sought its response on the plea by August 13.
The court initiated the public interest litigation (PIL) on its own by taking cognisance of five letters sent by seven undertrials facing trial for cases ranging from murder to drug possession and also under the Unlawful Activities (Prevention) Act (UAPA).
Ujair Ahmed, one of the undertrials who wrote to the court, was arrested in 2013 by the National Investigation Agency (NIA) for various offences under the UAPA and is lodged in the Rohini jail here for over five years.
However, the case was yet to be put on charge, he has said in his letter, while claiming that he was falsely implicated in it.
Another undertrial, Imran Khan, who is lodged in Tihar Jail here since July 2016, when he was arrested by the NIA for offences under the UAPA, has said in his letter that the chargesheet in his case was filed in July 2016, but since then, there has been no progress.
Shahjahan, Mohammad Sajid and Sattar, lodged in Tihar Jail, are facing a drug possession and trafficking case lodged against them in 2014. They have written in their letter that the matter is pending trial in the lower court, which has till date examined only eight of the 26 witnesses.
They have also sought a speedy trial in their case.
Shahbuddin, an accused in a 2015 murder case and currently lodged in Tihar Jail, has prayed for a speedy trial of his case, in which the lower court has examined only eight of the 20 witnesses till date.
A similar plea has been made by Shankar, accused in a 2014 rape case, who is also lodged in Tihar Jail. He has contended that the trial court has examined only nine of the 17 witnesses in the case till date.