Mr Singh was attending a function at the hospital
The office of the Indian PM has ordered a probe into an incident involving the death of a man during the PM's official visit to the northern Chandigarh city.
The family of the dead man says he was denied timely treatment at a hospital because of the security over the PM's visit to the city.
The hospital, where the PM was at a function, denied the charge.
Security for VIPs in India routinely leads to traffic being held up and public access to buildings denied.
A spokesman for Prime Minister Manmohan Singh's office has said he was "saddened" at the death of SP Verma at the hospital in Chandigarh on Tuesday.
"A full report has been asked for [from the authorities]," the spokesman said in a statement.
The family of the 32-year-old Mr Verma said that they failed to reach the emergency room of the hospital in time as the security personnel deployed for Mr Singh's visit sent them from one gate to another.
A family member told reporters that it took them "almost an hour and a half" to reach the casualty department because the security would not let them inside the hospital.
Mr Singh attended a function at the state-run hospital for 90 minutes.
A spokesman for the Post Graduate Institute of Medical Research hospital denied the family's claim and said no patient had been denied entry at any gate to the casualty department.
The spokesman said Mr Verma had "a history of end-stage kidney disease" and was "found dead" when he was admitted to casualty.
Correspondents say people in India are frequently held up in traffic and denied entry to public buildings because of heavy security during VIP visits.
Students have missed examinations and patients have died in ambulances in the past as they waited for vehicles carrying VIPs to pass.