SEOUL, South Korea — After years of trying to separate fact from propaganda about North Korea’s nuclear program, American and South Korean intelligence officials say they have concluded that the country can now mount a small nuclear warhead on short- and medium-range missiles capable of hitting much of Japan and South Korea.

The United States and its allies have sought for nearly a decade to prevent the North from gaining such capabilities, ever since it detonated its first atomic device a decade ago. Their failure is likely to raise new questions about the effectiveness of the policy toward North Korea, while ushering the long-simmering nuclear standoff with the North into a more perilous phase under its combative young leader, Kim Jong-un.

The assessment of the North’s new capabilities is not based on direct evidence from inside its nuclear program, senior officials said, but draws on intelligence gleaned from high-level defectors, analysis of propaganda images and data collected from North Korean missile and nuclear tests, which have accelerated over the past six months.

While some intelligence agencies suggested as early as 2013 that the North had learned enough about rocket engineering and the miniaturization of nuclear warheads to mount one on a shorter-range missile, there is a new consensus and greater confidence in that view in both Washington and Seoul, the officials said.