Buchenwald, near the city of Weimar, was the biggest concentration camp on German soil. Set up by Hitler's SS in 1937, it held more than 250,000 Jews, Roma, homosexuals and other people not tolerated by the Nazis. More than 56,000 people died there from torture, medical experiments and starvation.
European Parliament President Martin Schulz said in a speech in Weimar that in the 1930s people allowed the seeds of hatred to grow in their hearts, allowing the Holocaust to happen.
"To honor the victims...We want to fight the return of demons that we thought were overcome but which still show their ugly face - racism, anti-Semitism, ultra-nationalism and intolerance," said Schulz.
Although towns across Germany have seen similar attacks by right-wing radicals - Der Spiegel says there were 150 last year - the fire in Troeglitz caught the headlines.
"We must not let agitators and arsonists believe a silent majority stands behind them," said Schulz. "We must oppose xenophobia and say clearly that we, the majority, support refugees," he said.
Although Germany has also seen big counter-demonstrations and its popularity has waned, Dutch far-right politician Geert Wilders is to address marchers on Monday and may boost numbers.