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US President Barack Obama has warned that a nuclear-armed North Korea poses a "grave threat" to the world.

At a news conference with South Korean President Lee Myung-bak, Mr Obama said the US would "vigorously" pursue an end to the country's nuclear programme.

North Korea conducted an underground nuclear test on 25 May, before test firing a number of short-range rockets.

"Under no circumstance are we going to allow North Korea to possess nuclear weapons," said Mr Lee.

'Break the pattern'

Mr Obama said that he and his South Korean counterpart had agreed that a new UN resolution designed to halt North Korea's nuclear ambitions should be fully enforced.

And he pledged to end a cycle of letting North Korea create a crisis in order to be rewarded with concessions from the international community.

"This is a pattern they've come to expect," Mr Obama said.

"We are going to break that pattern."

Mr Lee was in Washington for talks with the US president.

The two men also discussed a free trade deal signed by the US and South Korea two years ago.

During last year's presidential election campaign, Mr Obama criticised the agreement, saying its terms were too favourable to South Korea.

In their meeting in Washington, the leaders agreed to initiate working-level talks to resolve their differences.