Tokyo (CNN) -- Airborne radiation levels continue to fall outside of the stricken Fukushima Daiichi nuclear plant, though serious concerns remain about potentially ominous breaches in reactor cores after water showed alarming radiation levels in tests of water at two locales.

An official with the Tokyo Electric Power Company -- which operates the facility -- told reporters Saturday that water samples from the turbine buildings for the Nos. 1 and 2 reactors similarly found high levels of radiation.

The readings, while high, were about half that detected earlier in the basement of the No. 3 turbine building, which officials10,000 times above normal. have said were

Hidehiko Nishiyama, an official with Japan's Nuclear and Industrial Safety Agency, said Friday that analysis of this tainted water suggests "some sort of leakage" from the No. 3 reactor's core -- signalling a possible break of containment vessel that houses the core.

As authorities work to determine the extent, root and ramifications of this water contamination spikes, Graham Andrew of the International Atomic Agency reported Friday that "there has not been much change ... over the last 24 hours" -- at least as far as negative developments suggesting any major new releases of radioactive material into the air.

In fact, the world nuclear agency noted on its website that on-site monitoring shows that measured radiation in and around the plant, which is 240 kilometers (150 miles) north of Tokyo, "continues to decrease."

Tokyo Electric reported on its website that, at 7 a.m. Saturday, radiation at the plant's main gate were 0.219 millisieverts per hour -- a fraction of the 400 millisieverts per hour measured between Units 3 and 4 on March 15, and a significant drop from readings taken at the same gate over the past week.

By comparison, people in industrialized countries are typically exposed to 3 millisieverts of radiation per year. Yet Japan's health ministry has said those trying to stem the crisis at the Daiichi plant can be exposed to 250 millisieverts total before they must be taken off the job.

This storyline, though, has largely taken a backseat to worries about the radiation leaks into the water -- and their effect on continued operations aimed at cooling nuclear fuel rods throughout the facility and preventing further radiation releases.

Work near the No. 3 reactor has been halted since three men laying cable stepped in highly contaminated water, according to the nuclear safety agency. Water is still being being pumped into the contaminated vessel.

The workers were exposed to between 173 and 181 millisieverts of radiation, in two cases when the tainted water rubbed against their skin. They have been admitted for a four-day stay at the National Institute of Radiological Sciences, a research hospital in Chiba, though experts noted that their injuries may not be more serious than a bad sunburn.

Moreover, evidence of radioactivity in the water around the plant is not necessarily surprising given the amount of water sprayed onto and pumped into the reactors, said Ian Hutchinson, professor of nuclear science and engineering at the Massachusetts institute of Technology.

"I am not particularly alarmed," he said.

Still, the incident raised questions about safety at the plant as more than 500 people -- including government authorities and firefighters -- continued working there Saturday.

The high measure prompted a top official with Japan's nuclear safety agency to urge Tokyo Electric to "improve its radiation management measures."

The No. 3 reactor is the same one cited in the dramatic evacuation last week of a small crew of workers who had stayed behind after the plant's owner pulled most employees from the area. The workers were pulled back March 16 after white smoke began billowing from the reactor and radiation levels spiked.

At the time, the Japanese nuclear safety agency said it suspected damage to No. 3's containment vessel, but a government spokesman the next day said there had been no indication of a "major breach of containment."

That reactor is of particular concern, experts have said, because it is the only one at the plant to use a combination of uranium and plutonium fuel, called MOX, that is considered to be more dangerous than the pure uranium fuel used in other reactors.

Plant workers also had already been watching the plant's No. 1 reactor, prior to the announcement of similarly contaminated water in its own turbine building. They had been concerned that an increase in pressure noted inside that reactor could be a troublesome sign. Earlier, buildups of hydrogen gas had driven up pressure that led to explosions at three of the nuclear plant's reactors, including the No. 1 unit.

Nishiyama conceded that "controlling the temperature and pressure has been difficult" for that reactor, which on Friday had been declared stable.

Authorities hope to start pumping in fresh water -- rather than the corrosive seawater they have been using -- to cool the spent-fuel pool at the No. 1 reactor and other locations.

Such pools have nuclear fuel rods that can emit radiation if the water that normally surrounds them leaks out or boils off, which is more likely to happen without any functional cooling system in place.

Switching to fresh water, instead of seawater, is also a priority for the No. 2 reactor's core (as well as for its spent fuel pool), Nishiyama said. The aim is to prevent further corrosion and damage inside, which may be worsened by the buildup of salt.

A U.S. military barge loaded with fresh water to help cool the reactors left Yokosuka Navy Base at 11 a.m. Friday, said Jose Schmitt, commander of Fleet Activities at Yokosuka.

A Japanese ship escorted the barge to the nuclear plant, with U.S. personnel are not involved in the escort or distribution of the water, according to Maj. Joseph Macri, a spokesman for U.S. Forces Japan.

The U.S. military assistance follows a request by Japanese government and utility authorities for large amounts of fresh water.

Efforts also continue at the Nos. 4, 5 and 6 reactors -- each of which have their own concerns, though less pronounced because the units were on scheduled outages when the quake struck. None of these three units had nuclear fuel inside their reactors, though efforts are ongoing to control temperatures inside the spent fuel pools.

On Friday morning, a concrete pump truck was used once again to inject seawater into the No. 4 unit's fuel pool.

CNN's Jennifer Rizzo contributed to this report.