The US goal of pressing North Korea to give up its nuclear programme is “probably a lost cause”, the head of American intelligence said on Tuesday in the frankest admission yet that the policy of three administrations towards Pyongyang has failed.

Although US officials insisted nothing had changed in the overall approach towards North Korea, director of national intelligence James Clapper said that the best the US could hope to achieve was a cap on the country’s nuclear capabilities.

Mr Clapper’s comments underline the reality that North Korea will be one of the most difficult problems to face the next president. Given the strides it has made in recent years to develop a nuclear missile that could reach the US, pressure is growing in Washington to find a new approach to the nuclear threat from North Korea.