WASHINGTON  Japanese officials issued broad evacuation orders on Saturday for people living near two nuclear power plants whose cooling systems broke down as a result of the earthquake. The officials warned that small amounts of radioactive material were likely to leak from the plants.

The power plants, known as Daiichi and Daini and operated by Tokyo Electric Power, experienced critical failures of the cooling systems after the plants were shut down, as they were during the quake.

About 45,000 people were affected by the evacuation order at the Daiichi plant, where those living within a six-mile radius were told to leave. The evacuation of the second plant was for a one-mile radius because “there is no sign that radiation has been emitted outside,” an official said.

Failure of the cooling systems allowed pressure to build up beyond the design capacity of the reactors. Small amounts of radioactive vapor were expected to be released into the atmosphere to prevent damage to the containment systems, safety officials said. They said that the levels of radiation were not large enough to threaten the health of people outside the plants, and that the evacuations had been ordered as a precaution.

Nuclear safety officials focused initially on the Daiichi plant. But by Saturday morning Japan had declared states of emergency for five reactors at the two plants, an escalation that added to worries about the safety of nuclear facilities in the quake-prone Japanese islands.

The Daiichi and Daini plants are 10 miles apart in Fukushima Prefecture, about 150 miles north of Tokyo and close to the quake’s epicenter off the coast.