Story highlights South Korean official tells CNN: We believe North has mid-range nuclear capability

Admits the assessment is not backed up by solid proof

News comes as 38 North notes "suspicious activity" at nuclear processing site

Seoul, South Korea (CNN) South Korea believes its neighbor to the north may be able to mount a nuclear warhead onto a medium-range missile.

In a background briefing with foreign reporters Tuesday, a government official said it appears North Korea has succeeded in miniaturizing a warhead enough to be mounted onto a Rodong missile.

The official -- who remains unnamed as per South Korean government protocol -- says this ballistic missile can deliver a one ton (907 kg) warhead a distance of 2,000 km (1243 miles), putting U.S. military bases in South Korea and Japan within range.

The official said: "We believe they have the ability to mount a nuclear warhead on a Rodong. Whether they will fire it like that is a political decision."

However, the official added they have no evidence to prove this capability, an assessment backed up by the United States.