International nuclear experts warned of the possibility of major accidents similar to the 1986 Chernobyl disaster in Ukraine and the 1979 partial core meltdown of the US Three Mile Island reactor.
Japan's top government spokesman said it was highly likely a meltdown had occurred in one reactor of the Fukushima plant and that it was working on the assumption that one may occur in another.
Chief Cabinet Secretary Yukio Edano added that the radiation released into the air so far had not reached levels high enough to affect human health.
The crisis started with Friday's massive quake and tsunami disaster, the worst on record in Japan, which caused electricity blackouts and led to malfunctions of the cooling systems of the plant's reactors.
Authorities immediately declared a nuclear emergency and have since scrambled to prevent two reactors from overheating by pumping in water and releasing steam to depressurise them.
Operator Tokyo Electric Power (TEPCO) took the drastic step of using sea water to cool reactor one -- where a huge explosion Saturday tore away the outer concrete housing while leaving the steel reactor intact.
On Sunday, the operator warned that another reactor, number three, was also overheating and that so much water had evaporated at one stage that the top three metres (10 feet) of mixed oxide (MOX) fuel rods were exposed to the air.
A TEPCO spokesman later told AFP that the rods were covered again.
Edano said the pressure build-up at reactor three had forced another release of vapor to depressurise the facility and that "we assume that a minute amount of radioactivity was released".
Nuclear plant operators must alert the government when the hourly level of radioactivity reaches 500 micro sievert -- and Edano said the level had topped 1,200 Sunday morning. It had hit just over 1,000 at one stage Saturday.
A TEPCO spokesman said Sunday: "Radiation levels declined late last night but rebounded this morning and topped the limit set by the government. So, we informed the government about the result in an emergency report."
The government has evacuated people from a 20 kilometre (12 mile) radius around the facility -- while also moving people out of areas surrounding a second nearby plant, Fukushima No. 2, which has four reactors.
A total of 22 people have also been hospitalised after being exposed to radioactivity, although it was not immediately clear to what degree they were exposed and what the condition they were in.
In the city of Fukushima, set amid mountains some 80 kilometres northwest of the seaside plants, fears grew about the nuclear plants, and people rushed to stock up on supplies. Petrol stations had already run dry.
Hundreds joined orderly queues outside a co-op market where shop assistants wore surgical masks and overalls, and shoppers came out carrying as many bottles of water, groceries and other supplies as they could.
Naruki Ono, 40, who had travelled 40 minutes to get to the town, said "people are nervous. People are not panicked, but nuclear plants are scary. The bottom line is: I will pray that the nuclear plant doesn't explode."
Japan's centre-left Prime Minister Naoto Kan, who was battling opinion poll ratings below 20 percent before the disaster struck, faced media criticism on Sunday over his government's response to the nuclear crisis.The Yomiuri Shimbun daily noted that it took five hours for the government to publicly address fears about a nuclear meltdown after the blast Saturday, while an Asahi Shimbun headline charged: "Crisis management all mixed up"