President Michael D Higgins said he has written to Greek President Prokopis Pavlopoulos to express his sympathies with the families of those who have lost their lives and livelihoods in the fires.
The fire department's special arson section, which probes all major fires, was conducting the investigation to determine how the wildfire started.
Fire service spokesperson Stavroula Maliri raised the overall death toll on Tuesday to 74 from an earlier count of 60.
Although it had abated by Tuesday afternoon, the blaze was far from extinguished and more than 230 firefighters were still trying to put it out, helped by volunteers and water-dropping aircraft. Numerous bodies were burned beyond recognition, making identification hard.
Relatives looking for missing loved ones have been heading to the morgues in Athens.
Earlier, rescue workers searching a cliffside in the seaside town of Mati found more human remains. He said: "Greece is going through an unspeakable tragedy".
The team includes veterans of such major disasters as the 2002 midair plane crash over Ueberlingen, Germany that killed 71 people and the 2004 Indian Ocean tsunami that killed at least 225,000 across multiple Asian countries. The flames this week were fanned by high winds.
He had tried to drive away with his mother, wife and 19-year-old son, but the fire was too fast.
A search and rescue operation is underway for them. Moraitis suffered burns to his leg from the heat of the air. Red Cross rescuers who found them said they appeared to be families or groups of friends, as they were found hugging in groups of threes and fours.
"I'm grateful to all of them", he said.
A toll-free number was also set up for those trying to report people missing in the fires.
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Nikos Stavrinidis had gone to his summer home in the Mati area near Rafina with his wife to prepare it for his student daughter who was coming to stay. Hundreds of volunteers lined up at the Rafina town hall to offer whatever help might be needed. Several of the dead were people who drowned. She hadn't heard from her since.
"We didn't all make it", Stavrinidis said. "It's just that we can't find her. ... I feel lucky to be alive". "Where she went, nobody knows where she went". "Nothing happened to her auto, the house was not burned, so where is she?" It has counted more than 20 fires across the country.
According to the Irish Daily Mail the couple married recently and became separated as they tried to escape the flames in the seaside resort of Mati.
However, the Irish Embassy in Greece yesterday confirmed the tragic news.
He said: "Following my visit to Greece and my meeting with him and the presidents of Italy and Portugal, I am very conscious of the resilience of the Greek people, who should be assisted by all of us in these hard times".
Some suggested that the sheer force of winds, thick pine, fire and panic was a deadly combination making even the most well-executed evacuation plan futile.
Flames rise as a wildfire burns in the town of Rafina, near Athens.
How are the authorities responding?
Greece's fire brigade said the intensity and spread of the wildfire at Mati had slowed on Tuesday as winds died down, but it was still not fully under control.
"People died for nothing!" one woman sobbed at the minister.
The actions of some residents had closed the roads to the beach, he argued.