It is President Roh's first visit to the United States
The South Korean President, Roh Moo-hyun, has arrived in the United States for a week-long tour which will include a key summit with President George Bush.
President Roh has a number of engagements in New York, before flying to Washington on Wednesday, where the issue of North Korea will be top of the agenda.
In his first public engagement in New York, President Roh urged North Korea to abandon its nuclear programme.
The BBC's Seoul correspondent described Mr Roh's visit as his toughest diplomatic challenge to date, as he tries to resolve the North Korean threat and repair relations with the US.
On the opening day of his US tour, President Roh made his feelings about the North Korean nuclear programme clear.
"For world peace and security on the Korean peninsula, North Korea must abandon its nuclear development and destroy whatever nuclear materials it possesses," Mr Roh said in a meeting with Korean residents of New York on Monday.
Both countries agree on the need to resolve the North Korean nuclear threat peacefully, but hardliners in the Bush administration have not ruled out a military option and are pushing for increased economic sanctions against the North.
Relations between the two countries were also soured by an upsurge in anti-American protests within South Korea.
The BBC's Seoul correspondent says that President Roh capitalised on this anti-Americanism when he called for a more equal relationship between Washington and Seoul ahead of his electoral victory in December 2002.
But now President Roh seems more willing to compromise, and has agreed on the need for a continued strong military alliance with the United States.
The two presidents are expected to issue a joint statement at the end of a summit calling for an outright rejection of a nuclearised Korean peninsula.
The BBC correspondent says that personal chemistry with President Bush could hold the key to whether Mr Roh is successful in repairing the strained relationship between the two countries.