Bush and first lady Laura Bush arrived in Singapore early Thursday and visited a museum before meeting with Lee at Astana, the official residence of Singapore's president.
Lee described the two men's relationship as "excellent," and said he and Bush had discussed regional matters, the Middle East, security issues and terrorism. He said the two countries' interests were aligned and joked that he and Bush had exchanged views so many times, "we know how each other thinks."
In turn, Bush thanked Lee for briefing him firsthand on events in the "neighborhood" of Southeast Asia.
Bush stopped in Singapore on his way to attend the Asia Pacific Economic Leaders meeting in Vietnam, which begins Friday.