Tokyo (CNN) -- Government and utility officials are still trying to figure out Monday what to do with highly radioactive water that's collected in several locales at the Fukushima Daiichi power plant, even as they deal with other problems including rising temperatures in one of the facility's nuclear reactors.

Hidehiko Nishiyama, an official with Japan's nuclear and industrial safety agency, said that as of Monday morning there is no place to put water that has pooled in the basement of the No. 2 reactor's turbine building. This is the same water that's been the source of considerable confusion of late, after the release of alarming -- and ultimately incorrect -- levels of radiation.

That water is giving off radioactivity at a level of 1,000 millisieverts per hour, an official with the plant's owner Tokyo Electric Power Company, told reporters.

This equates to more than 330 times the dose an average person in a developed country receives per year, and four times the top dose Japan's health ministry has set for emergency workers struggling to prevent a meltdown at the damaged plant. But Tokyo Electric said that figure is a mere 100,000 times normal levels for reactor coolant, not the 10 million times normal reported Sunday.

Japanese Chief Cabinet Secretary Yukio Edano said Monday that Tokyo Electric officials cited fatigue among its workers as a reason for the error.

"However, measurement of radioactivity is vital for the safety of the workers there," Edano told reporters. "So such a mistake is not something that should be forgiven or acceptable."

Also on Monday, Nishiyama said the plan is to pump tainted water out of the No. 2 turbine building's basement using what he called a condenser. But that apparatus is "almost full," as are several storage tanks nearby.

"So we will first have to empty some of the tanks," he said, without giving a timetable as to when this might occur. "Once that process is over, the puddle would be removed."

While high levels of radiation of water in the Nos. 2 and 3 turbine buildings (and, to a lesser extent, in the No. 1 unit) have been the chief focus of late, they aren't the only problems at the facility, which is 240 kilometers (150 miles) north of Tokyo.

Most of the concerns have centered around the Nos. 1, 2 and 3 units, which were the only ones operating -- and with active fuel rods in their reactor cores -- on March 11. The 9.0-magnitude earthquake and tsunami knocked out backup generators that ran their coolant systems and damaged water pumps at the plant, forcing workers to scramble to prevent a meltdown.

While there have been less alarms in recent days, that scramble is far from over. On Monday, for instance, Nishiyama noted that the temperature is rising inside the No. 1 reactor.

To address this issue, the flow rate of fresh water into the reactor core will be further adjusted, the nuclear safety official said. That water is being directed in via a fire truck and temporary electricity-driven pump, with a more permanent power generator likely in place by Tuesday.

Authorities plan to similarly get distinct power sources for the cooling systems for units Nos. 2 and 3 in the coming days. Fresh water is now being pumped into those two reactor cores as well, using the same fire truck set-up and temporary electrictity-powered pumps.

Between Monday and Tuesday, authorities hope to switch from using seawater to fresh water in these three unit's spent nuclear fuel pools, where some fuel rods are also located. Besides covering and keeping nuclear fuel cool, the fresh water ideally will flush out salt so the cooling systems can operate better.

The spike in heat at the No. 1 unit could be a sign that nuclear fuel rods are overheating. If those fuel rods are fully or partially exposed, that could lead to a buildup of pressure that could cause an explosion or the release of more radiation into the air, soil or water.

That's what experts fear has happened at the No. 2 reactor, after high levels of radioactive materials that are biproducts of the nuclear fission process were found in its turbine building's basement.

"The radioactive material that is found in that water is either from the reactor itself or the spent fuel pool," said Nishiyama. "At the moment, we consider that the possibilities are higher that the water is from reactor."

High radiation levels persisted in the Pacific Ocean waters near the seaside power plant, with one monitoring post reporting levels 1,850 times normal on Sunday.

However, Nishiyama told reporters Sunday that it was "not possible" that radioactive water was leaking into the ocean from the plant. He suggested runoff from the area around the damaged plant might have carried radioactive particles into the ocean, but said no definite source had been identified.

CNN's Whitney Hurst contributed to this report.