Civil Protection Minister Vassilis Kikilias said there had been several attempts by arsonists to start new fires on Mount Parnitha, north-west of Athens.
The blaze is one of hundreds in the nation where wildfires have already killed at least 20 people this week.
“You are committing a crime against the country,” Mr Kikilias said.
“Arsonist scum are setting fires that threaten forests, property and, most of all, human lives,” Mr Kikilias told Greeks during a televised emergency briefing on Thursday.
“You will not get away with it, we will find you, you will be held accountable.”
Summer wildfires are common in Greece and scientists have linked the increasing frequency and intensity of extreme weather events, including heatwaves, to climate change.
Stefan Doerr, who directs the Centre for Wildfire Research at Swansea University, says that more flammable landscapes – due to hot weather or poor vegetation management – mean that arson and other incidents can more easily turn into fast-moving wildfires.
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Police and Greek intelligence service EYP are investigating the incidents, AFP reported.
Government spokesperson Pavlos Marinakis told Greek public broadcaster ERT that of 140 wildfire-related arrests, 79 were related to arson.
Hundreds of firefighters across Greece have been battling deadly wildfires.
The large fire front which erupted on Saturday near the port city of Alexandroupolis has become the EU’s largest on record, according to European commissioner Janez Lenarcic.
Meanwhile, on Mount Parnitha near Athens, fires have been raging in a forest adjoining the capital, threatening a national park.
Earlier this week, the bodies of 19 people believed to be migrants, with children among them, were found near the Evros region of north-eastern Greece.