Lee met Hillary Clinton, the US secretary of state, on Monday and will also meet other senior administration officials on his three-day trip.
Observers say that during Lee's visit to Washington, the US is likely to pledge its continued commitment to protect the South should the North attack.
The US has stationed troops in South Korea since the end of the Korean War in 1953 and has about 28,500 soldiers there now.
Security forces stationed in and around the North-South border continue to be on high alert, and senior administration officials said on Monday that the US navy will be ordered to carry out "vigorous enforcement" to inspect North Korean ships at sea suspected of carrying arms or nuclear technology.
However, the navy is to ask permission and not forcibly board the vessels, the New York Times newspaper quoted the officials as saying.
If a ship's crew refuses an inspection request, it will be followed to its next port.
The action stops short of forced inspections that Pyongyang said would be regarded as an act of war.
Despite threats of further isolation, the North Korean government has vowed to build more nuclear weapons and start enriching uranium in response to a unanimous UN Security Council vote imposing new sanctions on the country.
On Monday, state-run television reported that more than 100,000 people attended a rally held at Kim Il-sung Square in Pyongyang to denounce the new UN sanctions against the North.
Kim Il-sung is the founder of North Korea and father of current leader Kim Jong-il.
Kim Ki-nam, the secretary of the Central Committee of the Workers' Party of North Korea, said at the rally that the UN resolutions were a "wicked pressure offensive opened by the US imperialists to disarm us, strangle our economy, and undermine our ideology and system".
"Our angry armies and people will respond with revenge against sanctions by the US imperialists and take an all-out confrontation against their confrontation," he said.