A bench of Justices G S Sistani and Chander Shekhar asked the Centre and the police to file their replies and status reports before the next date of hearing on August 11.
The PIL was initiated by the high court after the news report was brought to its attention by a lawyer who sought directions to hospitals, both private and government-run, not to deny treatment in such cases.
According to the report, a 57-year-old dhaba owner and his 26-year-old son were shot dead allegedly by five men after a dispute over a cooler in outer Delhi's Najafgarh area on the night of July 26.
The accused wanted the cooler to be turned towards them but the dhaba owner, Shyam Verma, and his son Mayank did not agree, which led to a fight.
While the dhaba owner died on the spot, his son succumbed to injuries later, the report had said.
The report had also quoted one of the relatives of the victims as saying that Mayank would have survived if the first hospital where he was taken would have admitted him.