So far 44 people are known to have died since torrential rains swept across one of the country's most popular seaside destinations.
"The lone efforts of the emergency situations ministry and the regional authorities are clearly insufficient," Mr Putin said, quoted by the Interfax news agency.
Flags have been flying at half mast across the devastated Krasnodar region, where the local authorities declared Saturday a day of mourning.
Officials say the bodies of 44 people carried off by swollen floodwaters have been retrieved, most of them tourists, but several people are still missing.
Villages and resorts, packed with holidaymakers, were engulfed by water as the rain caused rivers and lakes to burst their banks.
Debris
In Shirokaya Balka, a coastal resort, flimsy wooden homes and cars were carried out to sea as what witnesses described as "a wall of water" cascaded down a mountain on Thursday. The shoreline is now littered with debris.
"We have never had to deal with a tragedy like this before," Alexander Tkachyov, Krasnodar's regional governor told the ORT television channel.
At the height of the flooding, about 1,500 people were evacuated.
But many of the tourists and residents say they were neither warned about the impending floods, nor offered help afterwards.
Despite the devastation, some cafes and shops reopened on Saturday and state television showed tourists sunbathing and swimming as the weather cleared up.
Other weather flashpoints in Europe include:
Southern Europe has also been suffering bad weather.
Italian resorts have been hit by violent storms and in Venice heavy rains raised the sea level, sparking fears of flooding.
The Spanish region of Catalonia and the Balearic Islands have also been experiencing downpours.
Southern Russia has been hit hard by flooding in recent weeks.
Heavy rains in June left more than 100 people dead, and forced hundreds of thousands more to evacuate their homes.
At the time, government officials acknowledged public concern that rescue efforts had begun too late.