SEOUL, South Korea — South Korea has determined that North Korea is capable of mounting a nuclear warhead on its medium-range Rodong ballistic missile, which could reach all of South Korea and most of Japan, a senior government official said on Tuesday.

The government’s assessment, shared in a background briefing with foreign news media representatives in Seoul, followed a recent claim by North Korea that it had “standardized” nuclear warheads small enough to be carried by ballistic missiles. South Korean officials, like their American counterparts, have said that the North has made progress in miniaturizing nuclear warheads, but have been reluctant to elaborate.

But after four recent nuclear tests by the North, the latest on Jan. 6, some nongovernmental analysts in South Korea have said that they believe the North has learned how to fit its medium-range Rodong missile with nuclear warheads. The senior government official echoed that assessment, but did not provide any evidence of how the government has made its determination.

He did not say if the North had actually built such a warhead or simply had the technology to do so, but said the government did not have any evidence that the North had actually fitted miniaturized warheads onto a missile.