Mochiduki on Friday visited Fukushima Prefecture for the first time since assuming his post earlier this week.
He met Governor Yuhei Sato at the prefectural office.
Mochiduki said the government will never forget that accepting construction of the facilities was a very harsh decision for the local communities.
He said he will make every effort to establish a relationship of trust with the local communities through careful explanations.
Sato asked the minister to push on with the project in consideration of people living as evacuees.
Mochiduki said the government will work hard to enact legislation in the autumn Diet session to stipulate that the stored waste will be moved out of Fukushima Prefecture within 30 years.
The minister then met the mayor of Okuma Town, Toshitsuna Watanabe. The storage facilities will be built in Okuma and Futaba towns.
Mochiduki asked for cooperation, saying that the government will give detailed and easy-to-understand explanations to owners of land at the planned site and others concerned.
The mayor said the priority is to gain understanding from the landowners and that he hopes the government will perform its duty with clear explanations.