Bush originally negotiated the "Strategic Framework Agreement Between the United States of America and the Republic of Singapore for a Closer Cooperation Partnership in Defense and Security" with Lee's predecessor in 2003.
The two leaders held a brief news conference after their White House meeting.
"It (the agreement) builds on a very sound relationship and broadens and deepens it further," Lee said. "It enables us to focus more on anti-terrorism, on anti-WMD proliferation, as well as on other aspects of our relationship -- defense technology cooperation, military cooperation between our armed forces, and strategic and security exchanges. "
Bush described Singapore as a country "with an interesting position in the Far East" and praised the prime minister as a "strategic thinker."