The discovery of nuclear fission was published in early 1939. A few months later, information was published suggesting that more than two neutrons were released with every fission reaction, meaning that a chain reaction (and thus a bomb or a reactor) was possible.

This led scientists in many countries to petition their governments for funding and attention with regards to the military applications of atomic energy. These included:

• The United States, which you know about. Their initial program started in 1939, the Uranium Committee, was entirely exploratory/experimental and quite small, and was not dedicated to producing a bomb at all.

• The United Kingdom, who concluded by 1941 that atomic bombs would be build-able but that only the United States could pull it off. So they went to the US and convinced them to turn their small, exploratory program into a real bomb program. (Which didn't really get started until late-1942 and early 1943.)

• France, where scientists had first published on the chain reaction. They were initially interested in developing a reactor but knew about bombs. However when they were invaded by Germany this program stopped.

• Germany, where the Army helped coordinate research into military applications of fission, which included experimental/exploratory work into reactor development and the theory of the bomb. By 1942 they concluded that bombs would be too hard to build and that reactors were more relevant. They never even got their first prototype reactor working.

• Japan, where the military helped coordinate a few atomic energy programs. They were, again, entirely exploratory — they were interested in whether bombs were things worth worrying about. They concluded that even the United States couldn't build an atomic bomb. It did not get anywhere.

• The Soviet Union, which was aware of the possibility of atomic bombs and that the USA was building them (through spies and inference). They had no significant resources to spend on this during the war, however, so their wartime program was spent collecting foreign intelligence, planning a research program, and locating stores of raw uranium within the USSR.

So the short answer is, yes, half a dozen countries during World War II had government-sanction fission research programs. However except for the United States, none of them progressed beyond the exploratory, "is this something worth thinking about stage." Only the United States (with encouragement from the UK) thought that they needed to built a bomb during the course of the war, because they thought (incorrectly) that they were in a race with Germany to build one.

Leo Szilard who was Hungarian had a patent for the concept of the nuclear chain reaction - British patent 630,726 - in the thirties. European physicists were aware of using it as an explosive.

Germany attempted to build nuclear weapons however they suffered severe brain drain due to their anti-jewish policies. Many of the scientists working on the Manhattan Project were jewish refugees so kicking them out/hunting them was very counter-productive for the Germans.

Also they lacked the facilities to enrich the uranium in the amounts needed to test and field a weapon.

Source: Weapons of Mass Destruction by Robert Hutchinson