Many of the Left Party's leadership were senior figures in the old SED, which ruled East Germany as a single-party state. And the prospect of the party's return to power has caused alarm in some quarters.
The German President, Joachim Gauck, abandoned the role's traditional political neutrality to speak out against it.
"People of my age who lived through the GDR [communist East Germany] find it quite hard to accept this," he said, and questioned whether the Left Party "has really distanced itself from the ideas the SED once had about repression of people, so that we can fully trust it".
Angela Merkel, who grew up in the GDR, has said a government headed by the Left Party would be "bad news" for Thuringia.