At least 140,000 people in the 12 mile radius around the plant have been evacuated. Those in a 12 to 19 mile radius of the plant have been ordered to stay indoors.
The mayor of Minami Soma, a town within that radius, said that residents are being stigmatized, Japanese broadcaster NHK reported.
"We are being labeled as contaminated lepers," he said.
The mayor said that drivers are refusing to transport supplies to them, NHK reported.
As Japan continues its rescue efforts, strong aftershocks continue to jolt the nation. Two aftershocks of magnitude 6.0 have hit Japan in the last 24 hours.
The Japanese are also bracing for a cold snap. Rain and snow is expected in the north. The worry for some is whether the snow will be radioactive.
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ABC News' Jim Hill, Juju Chang, Martha Raddatz, Luis Martinez, Lauren Pearle, Sunlen Miller and The Associated Press contributed to this report.