A total of 19 tremors, with the strongest measuring 5.9 on the Richter scale and felt in Tokyo, struck from 11:15 am (0215 GMT) in Niigata prefecture, the Meteorological Agency said.

The quakes were so powerful that some frightened children ran out of their classrooms on a day that was supposed to mark the return to normal at schools.

"Because of the aftershocks, some schools will let kids go home earlier," a local education official said.

The official said 35 schools reopened Monday, the last of the prefecture's 832 public elementary and junior high schools to resume classes since the October 23 earthquake which killed 39 people.

Japan's public broadcasting network NHK said at least 13 people were hurt in the latest tremors, but none of the injuries were life threatening.

A tremor collapsed the walls of a building, injuring five children and a woman, a fire department spokesman said. Other injured included a 75-year-old woman who fell from her motorbike and a 68-year-old man rescued after a fall, officials said.

"I was so shocked. But everything's okay as all my things were already broken by the previous quakes," a woman in her 20s told NHK.

The initial tremor on October 23 registered 6.8 on the Richter scale and was followed by hundreds of aftershocks.

"I am so sick of aftershocks," a woman in her 50s told the station. "I just wanted to go home."

Last month's earthquake was Japan's deadliest in nine years and also injured 2,600 people.

One of the enduring symbols of the earthquake was two-year-old Yuta Minagawa, who survived four days under the rubble in a crushed minivan where his sister and mother died.

The body of his sister, three-year-old Mayu Minagawa, was cremated Monday a day after rescuers recovered it from under rocks.

The little girl's coffin, with flowers and dolls on top, was seen off by dozens of her kindergarten friends at her home in Uonuma.

"Thank you for coming today. Mayu can go to heaven now," said her father, Manabu, standing next to Yuta.

The October 23 earthquake for the first time derailed Japan's famed bullet train and the high-speed service to Niigata, 200 kilometres (125 miles) northwest of Tokyo, was temporarily halted as a precaution on Monday.

The Meteorological Agency warned Niigata residents to remain cautious for at least a month.

The strong tremors were caused because a geological fault in the area appears to have been pushed upward by compression, said Masahiro Yamamoto, the agency's chief monitor for earthquakes and tsunami tidal waves.

"We are seeing relatively frequent aftershock activities. Continued caution is necessary," he told reporters.

"We expect the aftershocks will eventually die down after going through phases of frequent and then slow activity," he said.

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