Hitler's Bomb - written by Berlin academic Rainer Karlsch and published on Tuesday - suggests the Nazis may have been closer to acquiring a nuclear bomb than previously thought.
No independent corroboration of the claims was available, and some experts have voiced scepticism.
But Karlsch says in the book that "Hitler's bomb - a tactical nuclear weapon with a potential for destruction far below that of the two American atomic bombs - was tested successfully several times shortly before the end of the war".
What Nazi Germany lacked was enough fissile material, such as enriched uranium, to make a full-size, functioning nuclear bomb, he adds.
The book cites post-war witness accounts and Soviet military intelligence reports to back up its theory of a 3 March 1945, experimental nuclear test blast at the Ohrdruf military training area - then run as a concentration camp by the Nazi SS - but offers no first-hand documentary proof.
Gerald Holton, a professor of physics and the history of science at Harvard University, said the main scientists in the Nazi atomic bomb programme never mentioned a test blast or having built a working nuclear reactor.
Allied intelligence eavesdropped on the scientists - including the effort's leader, Walther Gerlach - while they were interned at Farm Hall manor in England after the war.
"Hitler's Bomb - a tactical nuclear weapon with a potential for destruction far below that of the two American atomic bombs - was tested successfully several times shortly before the end of the war"
Rainer Karlsch, Berlin academic and author of Hitler's Bomb
Any claims of a Nazi test blast "would have to have a lot of documentary evidence behind it", Holton said.
"It also would have to be checked against the remarks that Gerlach made during his period at Farm Hall ... where none of that sort of planning was discussed by him or anyone else," he added.
Russian officials said they were unaware of any such test. "We do not have information that something of this kind happened," said Nikolai Shingaryov, a spokesman for Russia's Federal Nuclear Agency.
"Of course we don't know everything, but we don't have data about this."
Ohrdruf, located in the southeastern state of Thuringia, was a Soviet military base after the war.
"There was no German atomic bomb," said Mark Walker, a historian at Union College in Schenectady, New York, who also has written on the topic.
A US mission that arrived in Germany with American troops in 1945 to investigate the German atomic bomb programme and seize its leaders concluded that the Germans were nowhere near making a nuclear weapon.
The German device probably was a two-tonne cylinder containing enriched uranium. The amount of uranium was too small, meaning the conventional explosives used to trigger the device did not set off a vastly more destructive nuclear chain reaction, Karlsch said.
Witnesses reported a bright flash of light and a column of smoke over the area that day, and residents said they had nausea and nosebleeds for days afterwards, Karlsch says.
One witness said he helped burn heaps of corpses inside the military area the next day. They were hairless and some had blisters and raw, red flesh.
Soil samples that Karlsch had analysed for his book found the presence of radioactive elements not found in nature, such as cesium 137 and cobalt 60, he said.
German government officials could not immediately be reached on whether the site still posed a radiation hazard.
Karlsch, an economist, concludes that the blast killed several hundred prisoners of war and Nazi inmates forced to work at the site.
Two months later, on 8 May 1945, Nazi Germany surrendered after the Soviets captured Berlin.