In some respects, South Korea’s leader has had the kind of presidency Mr. Obama would like to have. With less strangling government debt and a society driven to transform itself, Mr. Lee has been able to pursue much of the “win the future” agenda that Mr. Obama has advocated.

South Korea, as Mr. Obama likes to point out, has a high-speed broadband network that reaches more than 90 percent of its people, compared with only 65 percent of Americans. A larger percentage of South Koreans than Americans graduate from college. At a time when financially struggling school districts here are laying off teachers, South Korea is hiring them to satisfy demanding parents.

Indeed, Mr. Obama cites Mr. Lee’s views on education in virtually every speech he gives these days, including one in Pittsburgh on Tuesday, holding up the hard-working Asian country as an example of what the United States needs to do.

The two men have also built a personal bond, with Mr. Lee being among a small number of leaders — Chancellor Angela Merkel of Germany and Prime Minister Recep Tayyip Erdogan of Turkey are two others — who seem to have pierced the president’s reserve. At a lunch in Seoul in November 2009, which aides said left a lasting impression on Mr. Obama, the two spent much of the time discussing education, not least the role of parents in schooling their children.

“They were discussing the place that teachers occupy in society,” said Daniel R. Russel, Mr. Obama’s senior adviser on Asia at the National Security Council, who attended the lunch. “It was very human, and it’s not that common at those rarefied heights of leadership to have a real conversation in which the two people can speak openly about an issue they both care deeply about.”

Mr. Obama, Mr. Russel said, also admires Mr. Lee for his determination to thrust South Korea into the front rank of world powers and his approach to his erratic neighbor, North Korea. While he has taken a tougher line than his predecessors toward the government in Pyongyang, he has also stopped short of military action in response to a string of belligerent acts, including the torpedoing of a Navy ship and the shelling of a South Korean island.

During that tense period, Mr. Obama met Mr. Lee at a Group of 20 meeting in Toronto, and declared afterward, “My personal friendship with President Lee and my admiration for him continues to grow.”

That kind of emoting is rare for the president, who has been criticized in some quarters for not having the chummy relationships with foreign leaders that George W. Bush and Bill Clinton did. And the two leaders are not an obvious match: although both rose from modest circumstances, Mr. Lee, 69, spent most of his career running a construction and engineering conglomerate.

“When Obama deals with foreign leaders, he tends to be very transactional,” said Victor D. Cha, a former Asia adviser in the Bush administration who teaches at Georgetown University. “But there’s absolutely no doubt that he has really connected on a personal level with this leader.”

Mr. Lee has not had an easy time as president, but, of course, that may only serve as more common ground for the two presidents. Elected in late 2007 by a wide margin, with a pledge to revive the economy, he cast himself as a pragmatist — which is perhaps Mr. Obama’s favorite self-description.

Yet Mr. Lee has had an even rockier time in the public-opinion polls than Mr. Obama, first struggling with street protests over imports of American beef and, to this day, fending off criticism of his business ethics. Mr. Lee, however, does not have to worry about re-election; by law, South Korean presidents are limited to a single five-year term.

A long delay by the United States in ratifying a free trade agreement has also frustrated South Korea and prompted a tense exchange between Mr. Lee and Mr. Obama at a Group of 20 meeting in Seoul in 2010. The Senate and House both voted to approve the pact Wednesday. (While the votes were being cast, Mr. Lee and Mr. Obama were dining together at a Korean barbecue restaurant, Woo Lae Oak, in the Virginia suburb of Tysons Corner.)

The Obama administration, however, has steadfastly supported Mr. Lee in his dealings with Kim Jong-il, the North Korean leader, helping South Korea with an investigation of the sinking of its ship, the Cheonan, and staging naval exercises in the Yellow Sea to deter the North. And the administration took an immediate liking to Mr. Lee’s harder-line approach to the government in Pyongyang, which made offers of aid contingent on Mr. Kim’s abandoning his nuclear ambitions.

“The feeling was, ‘This guy’s approach on North Korea is right on the money, and it’s our approach,’ ” said Jeffrey A. Bader, who was Mr. Obama’s chief adviser on Asia at the National Security Council until April.

American officials said this support has allowed Mr. Lee to respond to North Korea sternly but without risking a deadly confrontation. Indeed, after quiet pressure from American diplomats, Mr. Lee has dropped a demand that North Korea apologize for sinking the Cheonan — which it denies doing — as a condition for any new talks between the North and South.

Now that those talks have resumed, the United States has also reopened contact with North Korea. A second meeting between the administration’s special envoy, Stephen W. Bosworth, and a senior North Korean official is likely to be announced after Mr. Lee’s visit, administration officials said.

Few Americans hold out much hope for a breakthrough with North Korea. But that will have little impact on Mr. Lee’s visit, which, coming on the heels of Congressional approval of the trade pact, will serve as a reminder of the alliance between the United States and South Korea.

“Lee Myung-bak is the most dynamic leader in that region right now,” said Michael Green, a senior Asia adviser in the Bush administration. “There’s a lot to like about him for the White House.”