Over 110,000 members of the police, fire fighting and Self-Defence Forces were taking part in the operations, Efe news quoted public broadcaster NHK as saying in a report.
Rescue efforts could be hampered as rain is forecast in the affected areas on Monday evening and authorities have asked people to exercise caution amid increased risk of flooding and landslides following record rainfall due to the passage of the typhoon.
The government has also asked people to stay away from dangerous areas such as rivers and mountain slopes.
The death toll due typhoon Hagibis' passage through Japan climbed to over 30 on Monday morning.
While NHK has reported at least 31 dead, Japan's Kyodo news agency said that it has killed at least 35.
Around 20 people were also reported missing and about 200 have been injured, according to the figures of rescue teams and local authorities.
The passage of Hagibis - the 19th typhoon of the season in the Pacific and one of the most powerful to hit Japan in decades - caused record rainfall in some areas of the archipelago and heavy rains in large parts of the country.
The rains also caused numerous dams located along at least 21 rivers in the country to collapse, according to the Ministry of Land, Infrastructure, Transport and Tourism.
Nagano prefecture was among the worst affected by flooding due to the overflow of the Chikuma river, which flows through the region, leaving its residents stranded until they were rescued by helicopter and boats.
( With inputs from IANS )