The first and second division clubs held an emergency meeting at the J.League's headquarters in Tokyo on Tuesday and ruled out matches scheduled for April 2 and 3, reports said.
"I knew right away this was no ordinary earthquake," Kashima Antlers president Shigeru Ibata told the Kyodo news agency.
"There's no telling when we can restart the league again. The situation is getting worse by the day. Most of the people on the committee agree that the first week of April is already out of the question."
On Monday, the J.League postponed all March fixtures but said it was hopeful of restarting the season at the start of next month.
Since then, fears of radiation leaks from a nuclear plant in Fukushima Prefecture have grown as the country struggles to come to terms with Friday's 9.0 magnitude quake and tsunami that has estimated to have claimed at least 10,000 lives.
With radiation leaks reaching as far as the greater Tokyo region, many clubs cancelled training on Tuesday, with Kashima opting to disband until further notice along with reigning champions Nagoya Grampus.
Ibata questioned the use of electricity during the existing power shortage to organise football matches.
"Whether we play at night and use the floodlights or not, an enormous amount of electricity is used to host one match," he added.
"In these circumstances when we're short on electricity, it wouldn't be right to be playing.
"It's about timing. There will come a time when we start up again, to help get the country back on its feet through sports. But now is clearly not the time."
Ibata said the players, especially the overseas signings, have been frightened by the rising radiation levels and those who lived in the club dormitory were struggling to lead ordinary lives.
"There's no water at the team dorm," said Ibata, who made it clear he did not want to play the season away from Kashima in a temporary home.
"There's no food, no shower, no laundry. It's been like that for four days. The players are stressed out. They can't train at the clubhouse, and they can't train at the stadium. They trained on an artificial pitch used for the public yesterday."
The latest development raises further doubts over the prospects of Japan hosting international friendlies against Montenegro and New Zealand at the end of this month.
On Sunday, the Japan Football Association (JFA) insisted the matches would go ahead as planned before backtracking by stating they were "keeping their options open" a day later.
A decision on the fate of the friendlies is expected on Wednesday.
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