Seoul and its Western allies have failed to stop North Korea's weapons programme and Pyongyang says it will never give up its nuclear arsenal.

"Whether to gain leverage in talks with the United States or to secure its own regime, North Korea has kept developing intercontinental ballistic missiles (ICBM) capable of carrying nuclear bombs to the US," President Lee Jae Myung said during a visit to the New York Stock Exchange.

"It does not seem to have succeeded yet, but it is said to be at the final stage, with only the re-entry technology left and that too looks likely to be solved," he said.

Since taking office in June, Lee has reversed the stance of his hawkish predecessor and vowed to improve ties with North Korea.

Speaking in New York, he said that "the goal should be to freeze nuclear development, ICBM development and exports".

Halting further production and development of nuclear weapons would bring "major security gains", he said.

The South Korean president estimated his northern neighbour was producing enough material for "about 15 to 20 additional nuclear bombs each year".

"If left unchecked, the number of nuclear bombs would keep growing each year and its ICBMs would become more advanced," he said.

North Korean leader Kim Jong Un has ruled out denuclearisation and has strengthened military ties with Russia in recent years.

Kim said this week that he was open to talks with Washington, but only if he can keep his nuclear weapons, according to the official Korean Central News Agency.