Ukrainian emergency services said fires initially broke out on Saturday afternoon near the village of Vladimirovka, which is within the uninhabited Chernobyl exclusion zone.
On Monday, firefighters said they had been able to put out the smaller of the two fires, which engulfed around five hectares of land. The second, meanwhile, continued burning, covering a further 20 hectares.
Egor Firsov, head of Ukraine's ecological inspection service, referred to the situation as 'difficult' in a post on Facebook, where he also shared a short video of a Geiger counter showing radiation at 16 times above normal levels.
"There is bad news - in the centre of the fire, radiation is above normal," he wrote.
"As you can see in the video, the readings of the device are 2.3, when the norm is 0.14. But this is only within the area of the fire outbreak."
Vladimirovka is part of the deserted 1,000-square-mile exclusion zone - famously evacuated after the 1986 explosion at the Chernobyl Nuclear Power Plant, which exposed vast areas to dangerous levels of radiation.
Since then, the forested area around the power plant has been somewhat taken over by nature - meaning forest fires aren't uncommon.
"The problem of setting fires to grass by careless citizens in spring and autumn has long been a very acute problem for us," Firsov continued.
"Every year we see the same picture - fields, reeds, forests burn in all regions."
Firsov also called for new legislation that would impose harsher penalties for anyone who starts a fire in the area, adding: "There are relevant draft bills. I hope they will be voted in. Otherwise, large-scale fires will continue to occur every autumn and spring."
According to the Associated Press, police said they have tracked down a person suspected of starting the blaze after setting dry grass on fire.
The 27-year-old man said he burned the patch of grass 'for fun', and had failed to extinguish the fire when it began to expand quickly thanks to the wind.
While radiation in the area has substantially exceeded usual levels, emergency services said the radiation levels in the capital, Kyiv - which is around 100km south - were within norms.
Ukrainian police said that they have increased patrols in the area around the Chernobyl zone to prevent new fires.
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