Neither country would take the US' word for it without independently verification by their own intelligence agencies. In fact, they probably have better intelligence on the ground that we do.
So far as I have heard, the North Korean's have admitted to a uranium enrichment program. This does not mean that they have a bomb. However, even highly enriched U235 is not a particularly good bomb making material. Pu239 is much preferred. Also, uranium which has been only moderately enriched cannot be used to make a bomb, but it is useful in making nuclear reactors -- which North Korea needs in order to be self-sufficient in power generation.
Uranium has become an alternative to Plutonium because the extensive Plutonium production facility cannot be used due to '94 treaty. N. Korea has unranium mines. There are 4 million metric tons of uranium ore which can be readily mined. The uranium enrichment facility is smaller than plutonium production one, and easier to hide.
The local Korean paper reports that America suspects that the most likely candidate is the Pyongsung research complex outside Pyongyang, which is officially for IT research. It could have a small lab which does uranium enrichment, according to U.S. intelligence.