The death toll from Friday's quake in Elazig province had reached 39 people as hopes dimmed of finding more survivors amid the rubble.
The Ankara prosecutor's office is checking 50 individuals on suspicion of "spreading fear and panic" and "insulting the Turkish people, the Turkish republic and the state institutions", the Hurriyet daily said.
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The suspects are accused of sharing fake images about the quake on social media.
Turkish authorities were winding up their rescue efforts on Monday.
Interior Minister Suleyman Soylu told reporters that 24,000 tents had been provided, 1,000 container shelters were being built, and funds released to repair damaged buildings.
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Thirty-five of the victims died in Elazig and four in the neighbouring province of Malatya, officials said.
Health Minister Fahrettin Koca said 86 injured were still being treated in hospitals -- 18 of them in intensive care units.
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