US President George W Bush has said North Korea must live up to its promise to end its nuclear weapons programme.

He said the poverty-stricken country could share in South Korea's economic prosperity if it took concrete steps.

But Mr Bush, who is in South Korea on a three-nation Asian visit, made it clear the reclusive communist country must continue to live up to its step-by-step denuclearisation process agreed in six-party talks involving both Koreas, the US, Japan, China and Russia.

While he spoke of a future in which North Korea is no longer a part of his "axis of evil" - first outlined in 2002 along with Iran and pre-war Iraq - Mr Bush said much work remains, including improvement of Pyongyang's human rights record.

North Korea expects Mr Bush to remove it from the US list of terror-sponsoring countries as soon as next weekend, as promised when the hermit kingdom blew up its nuclear reactor cooling tower in June.

But Mr Bush said North Korea, which has a history of unpredictability and has repeatedly used negotiations over its nuclear program to wring aid and concessions from the West, must first agree to international terms for verifying its dismantlement efforts.

Even if Pyongyang is removed from the terror list, it will still be the most sanctioned country in the world, he added.

Meanwhile, Mr Bush has advised China that its pre-Olympics crackdown on dissent was "a mistake."

The communist country considers the Olympics a source of huge national pride and is pulling out all the stops, including rounding up and arresting some dissidents, to ensure no embarrassments when it gets under way on Friday.

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