If the affair "is resolved swiftly and they are returned as swiftly as possible, that could turn into something very positive for our bilateral relations," Turkish ambassador Kerim Uras told reporters in Athens.
"But if that's not the case, I fear it will not help at all, and that the public mood (in Turkey) will be affected," Uras said.
"I hope we will manage to swiftly go through the phases of due process and manage to return these terrorist elements so that they will face justice," he added.
"I think it was a mistake to accept them in the first place," the ambassador said, arguing that Greek authorities could have asked the helicopter to land near a Turkish facility.
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According to their lawyer, Ilia Marinaki, the Turkish soldiers -- two commanders, four captains and two sergeants -- fear for their safety and that of their families after the failed coup attempt against President Recep Tayyip Erdogan.
To block their deportation to Turkey, they have applied for asylum in Greece.
Uras bristled at the suggestion that the officers would not be treated fairly at home.
"We take offence at such reporting because needless to say, they will face a fair trial. It will be totally transparent," he said.
But he added that legal cooperation between both states was good and "we have full confidence in the Greek judicial system."
A mass crackdown by Turkish authorities on instigators of Saturday's attempted coup has fuelled fears Ankara may enact harsh retribution and even reintroduce the death penalty, abolished in 2004.