Hitler's father, Alois, was an illegitimate child whose own father was unknown, Austrian historian Roman Sandgruber told AFP.
Sandgruber, who last year published the first biography of Alois Hitler, explained that the rumours first began circulating in the 1920s, as Adolf Hitler began his rise to power.
The theory was encouraged by Hitler's political rivals as the Nazi leader took control of Germany in 1933.
Then after World War II, the memoirs of Nazi war criminal Hans Frank, who governed occupied Poland during the war, revived the story.
In his memoirs, published after his 1946 execution for war crimes, Frank said he had secretly researched Hitler's ancestry at the request of the Nazi leader himself.
"This must have been towards the end of the 1930s," wrote Frank, in an extract published by Germany's Der Spiegel magazine at the time.
Hitler, he said, had told him he was being blackmailed by a nephew over the matter.
Hitler's paternal grandmother Maria Anna Schicklgruber gave birth to Alois in 1837.
Frank claimed to have discovered that, at the time, she was employed as a cook for a Jewish family by the name of Frankenberger, in the Austrian city of Graz.
Her employer had paid her maintenance until Alois reached the age of 14, wrote Frank, claiming that an exchange of letters between her and the family proved this.
Frank said Hitler had told him that actually his grandmother and her future husband had let the Jewish man think he was the father in order to get the money out of him.
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Prime Minister Naftali Bennett denounced Lavrov's comments as "lies", and the foreign ministry has summoned Russia's ambassador for an explanation.
Israel's Foreign Minister Yair Lapid on Monday condemned Lavrov's remarks as "an unforgivable and outrageous statement as well as a terrible historical error.
"Jews did not murder themselves in the Holocaust," Lapid added. This kind of claim was the worst kind of anti-Semitism, he said.