Exception should be made to the restriction on withdrawals in the case of depositors who have pressing medical needs such as kidney transplant, he said at a press conference here.
The issue of the scam at the bank -- pegged by the investigative agencies at Rs 4,355 crore -- would rock Parliament's winter session, Singh said.
The Reserve Bank of India has capped deposit withdrawals at Rs 40,000 for account holders because of liquidity issues. The bank's troubles are attributed to mammoth loan defaults by real estate group HDIL.
"I do expect the Government of India, the RBI and the Government of Maharashtra to put their act together and provide a credible, pragmatic and effective solution to this case where 16 lakh depositors are crying for justice," Singh said.
The economist-turned-politician also said that people are dying of shock, in an apparent reference to three PMC Bank depositors dying this week -- one of them allegedly committing suicide.
Among the depositors, kidney patients waiting for transplant should be allowed to access their funds beyond the RBI-imposed cap, and if the need be, aid should be given from the Prime Minister's Relief Fund for meeting medical needs, he said.
Singh, who was once governor of the Central bank before his entry in politics, maintained that the RBI is a "great national institution", and hoped that it will find the required solution to the crisis.
But the government must strengthen the deposit insurance architecture too, he said.
Meanwhile, in a video doing rounds on messaging apps, a group of depositors who had gathered outside the corporate branch of the PMC Bank in suburban Bhandup, threatened a "Mumbai Bandh (shut-down)" if they did not get their money back by October 31.