Kefalogiannis said the powerful winds, estimated at force six on the Beaufort scale, were making the situation “very difficult”.
“If the wind dies down a bit, we might be able to get this fire under control. But the wind really hasn’t dropped,” he said.
A Greek Government spokesman said: “The situation remains critical as firefighting forces are still dealing with many active fronts, several of which are near hamlets.”
Greek authorities suspect that arson may be to blame, and have launched an investigation. They said it was suspicious that fires broke out on three different fronts at about the same time.
Kefalogiannis said there would be “heavy criminal sanctions” for anyone found to have lit fires deliberately.
Firefighting teams are trying to prevent the blazes from spreading to rural areas known for producing mastiha, a natural resin harvested from mastic trees.
On Sunday, about a dozen areas and hundreds of asylum seekers at a reception centre were forced to evacuate as the fires spread.
The fires on Chios are the most serious in Greece so far this summer, Greek media reported. Smoke has reached the island of Mykonos, far to the south, which is hugely popular with cruise ship passengers and tourists.
Although wildfires are common in Greece during the summer, experts say global warming is producing bigger and more frequent conflagrations. In 2023, devastating forest fires broke out on the island of Rhodes, forcing 19,000 people to flee the island.
Greece has hired a record 18,000 firefighters this year amid concerns that it faces a challenging fire season.
A heatwave is predicted in the next few days, with temperatures of more than 40C (104F) expected, including in the capital, Athens.