Last Saturday, 23 elderly people were killed when a fire swept through a wooden building at a care home in the Republic of Komi. Three people were rescued from the blaze.
"Those guilty must be brought to account," the president said at Thursday's meeting on the incident.
The president has instructed his administration to carry out comprehensive checks nationwide to uncover possible violations of law and to look into general living conditions. The inspections are likely to be carried by the administrations of regional presidential envoys along with federal agencies and regional authorities.
"These events should take place within a month and then I must receive a report on the issue," Medvedev said.
The president had already ordered the government to carry out a thorough investigation of the incident and dispatched a special envoy to investigate the case.
"As far as I understand, this care home was not even legally registered. It was a 'phantom' where people lived and died. We must investigate it thoroughly," Medvedev said on Thursday.
Nikolai Basmanov, head of the regional investigation department, said the cause of the fire could have been arson to conceal evidence of a murder. At the same time, he said, careless smoking was among the main possibilities being examined by investigators.