Tokyo Electric Power Co. said the rods may have melted after being fully exposed because of a low level of cooling water, Kyodo News reported.
Workers have been inside the No. 1 reactor building for about two weeks, attempting to restore its cooling system, which was knocked in the country's March 11 earthquake-tsunami disaster, the report said.
New data showed the water level in the pressure vessel needed to keep the rods cool is lower than earlier thought.
Efforts to restore normal cooling in the reactor have been progressing, the utility has said.
Separately, Kyodo quoted government sources as saying a planned investigation into the Fukushima nuclear crisis will take about a year.
An independent panel to investigate the crisis will have about 10 members, including scholars, legal experts and people from Fukushima prefecture where the plant is located.
As the recovery effort entered a third month, Prime Minister Naoto Kan said Japan will abandon plans to build new nuclear reactors and will "start from scratch" to come up with a new energy policy. Last year, the government announced plans to build 14 more nuclear reactors by 2030 to increase the share of nuclear power in Japan's electricity supply to 50 percent.
The government was working on a plan to help Tokyo Electric Power meet its payments to compensate those affected by the crisis. The cost could run into the billions of dollars.