North Korea receives birthday greetings to its leader Kim Jong Un from US President Donald Trump, but their personal relationship is not enough for a return to talks, according to a statement published by state news agency KCNA.

A North Korean diplomat who was until recently acting ambassador to Italy has gone missing, a South Korean member of parliament says, after a South Korean newspaper reported he was seeking asylum in the West.

US President Donald Trump, who has agreed to meet with Kim Jong Un, says there is a now a good chance the North Korean leader will give up his country's nuclear weapons.

Kim Jong Un warns the United States that he has a “nuclear button” on his desk ready for use if North Korea is threatened, but offered an olive branch to South Korea, saying he was “open to dialogue” with Seoul.

US President Donald Trump dismisses the prospect of talks with North Korea as a waste of time a day after Secretary of State Rex Tillerson said the US was maintaining open lines of communication with North Korean leader Kim Jong Un.

North Korean leader Kim Jong-Un says the country's second ICBM test demonstrated the ability to strike any target in the United States, in a direct challenge to President Donald Trump who issued dire warnings over its missile program.

South Korea's foreign minister says that North Korea's nuclear capability is expanding fast, echoing alarm around the world over the isolated state's fifth nuclear test carried out in defiance of UN sanctions.