According to police, Om Prakash (50) today succumbed to his injuries during treatment following the mishap last evening in the Vishnu Garden area of west Delhi.
A young girl is "still suspected to be trapped under the debris" and rescue efforts are on at the site of the building collapse, said Joint Commissioner of Police (West Delhi Range), Dipendra Pathak.
Delhi government, which has ordered an inquiry into the incident, accused the BJP-led MCD of failing to ensure compliance with safety standards, charges which the civic body denied.
"People have told me there was construction going on and the entire building has collapsed on one side due to which four people have died and eight others were injured," said Delhi PWD Minister Satyendera Jain.
"Whatever construction work was going on, MCD had full responsibility to stop it, which they should have done... The government has ordered an investigation, to be done by the DM of the area, and the report will be submitted within seven days," he said, adding that "strict action will be taken against the culprits".
Meanwhile, DCP (West Delhi), Pushpendra Kumar, said that an FIR "under Section 304 of IPC (causing death by negligence) has been registered against unknown persons in connection with the wall collapse".
As AAP held the civic body responsible for the tragedy, the BJP-led SDMC refuted the allegations and claimed it was "seepage in the sewer line" that had "weakened" the foundation of the building, leading to its collapse.
According to SDMC, the building was 25 years old and "no buildings laws were violated" as alleged by AAP.
"A sewer line was laid in the area about it three months ago; seepage in it weakened the foundation of the building, which led to the collapse," a senior SDMC official claimed.
Delhi's Public Works Department Minister Satyendra Jain announced an ex-gratia of Rs.2 lakh for next of kin of those killed and Rs.50,000 for the seriously injured.
"A magisterial probe has been ordered to find out the actual culprit," Jain said at the site on Sunday. He said the report would be submitted in a week.
Police suspect the building, located in a narrow lane, was illegally built.