The government hopes to finish 30,000 of the homes by the end of May.
About 135,000 people are living in shelters set up in schools and community centers.
Many others have moved into temporary housing or are staying with relatives.
Prime Minister Naoto Kan also approved an extra budget worth $50 billion to help finance disaster reconstruction.
The twin disasters destroyed roads, ports, farms and homes and crippled a nuclear power plant.
The government said the damage could cost $309 billion, making it the world's most expensive natural disaster.
Recovery efforts have been complicated by the crisis at the Fukushima Dai-ichi nuclear power plant, which lost its power and cooling systems in the earthquake and tsunami, triggering fires, explosions and radiation leaks in the world's second-worst nuclear accident.
Plant operator Tokyo Electric Power Co. said it will take six to nine months to bring the plant under full control.
The Associated Press contributed to this report.
