Kan told local leaders of Miyagi prefecture that the government has set an immediate goal of building 70,000 temporary houses and will speed up construction as much as possible.
The prime minister said the government will convene a panel of experts this week to study a blueprint for reconstruction.
Kan later surveyed areas that suffered extensive damage and visited evacuees at a shelter.
Meantime, U.S. Marines trained to rescue people in chemical, biological or nuclear emergencies held drills this weekend with Japanese counterparts.
So far, 13,000 deaths have been confirmed, but many bodies have likely washed out to sea and will never be found.
Another all-out search is on in Japan for the bodies of earthquake and tsunami victims.
"A month after the earthquake and tsunami, many people are still missing," said Japanese defense ministry spokesman Norikazu Muratani. "We would like to do our utmost to find bodies for their families."
Also, 250,000 households in northern Japan are still without running water and electricity as of Sunday.
As for the stricken nuclear plant in Fukushima, workers are still struggling to cool down its three reactors, four weeks after the earthquake and following tsunami knocked out the plant's coolant and backup power systems.
Meantime, one of the biggest concrete pumps in the world left LAX for Japan. It will be used to help contain the disaster at the Fukushima Dai-ichi plant.
The pump, which can be operated by remote control, will help cool the plant's nuclear reactors. A similar pump was also shipped to Japan from Atlanta.
In Tokyo, hundreds of protesters took to the streets on Sunday calling for an end to the use of nuclear power in Japan.
They marched in front of government buildings, the nuclear and industrial safety agency's offices and the headquarters of Tokyo Electric Power Company, which operates the Fukushima plant.
Many carried signs while others shouted "No more Fukushima."
The Associated Press contributed to this report.