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The man is coming back from an injury.
The world number four is unsure if he will be able to play at the Australian Open.
Greece's Tsitsipas was defeated by Argentina's Diego Schwartzman in his first singles match since elbow surgery.
He sat out his first singles match to protect his elbow.
He said he was in a lot of pain after playing in the doubles.
The Australian Open starts in January.
"That is enough time to recover, I believe," he said. I don't know, I haven't had this kind of injury before. It's my first time in this situation.
The 29-year-old rallied to win the match and secure victory for Argentina, after he was defeated by the 21-year-old.
His team-mate, Federico Delbonis, beat Greece's Michail Pervolarakis.
Schwartzman was trying to think that it was his first match since he injured his elbow.
I think I was ready for it. I found a way to get through it, even though playing against Stefanos was not easy.
Argentina will face Poland on Wednesday in their final group D match with a place in the semi-finals up for grabs after Poland beat Georgia.
Georgia's Aleksandre Metreveli, the world number 570, was beaten by Poland's Hubert Hurkacz, the world number nine.
Spain defeated Norway in straight sets thanks to the victories of Pablo Carreno Busta and Roberto Bautista Agut.
Carreno Busta beat Viktor Durasevic 6-3 6-3 and Bautista Agut upset Norwegian world number eight Casper Ruud.
After the singles rubbers, the match will go to the deciding doubles with the score tied at one.
Dusan Lajovic was forced to retire from his match with Cristian Garin due to an injured ankle after Serbia's Filip Krajinovic defeated Alejandro Tabilo.