The previous visit by a U.S. president was in 2001, when then-President Bill Clinton visited the country, six years after Washington and Hanoi normalized diplomatic ties in 1995.
Bush held talks separately with Vietnamese President Nguyen Minh Triet, Prime Minister Nguyen Tan Dung and Communist Party General Secretary Nong Duc Manh following a welcome ceremony at the Presidential Palace.
''I look forward to continuing to work to make sure our bilateral relations are close,'' Bush said at a brief photo session with Triet.
''I have seen now firsthand the great vibrancy and the excitement that's taking place in Vietnam,'' he said. ''You're like a young tiger.''
According to the joint statement, Bush and Triet expressed satisfaction at the progress made by the bilateral relationship, which it described as ''multifaceted and forward looking.''
''It encompasses significant and growing trade and economic ties, an emerging military-to-military relationship, successful cooperation on health and development issues, growing cultural and educational links, a commitment to resolving remaining issues stemming from the war, a shared interest in ensuring peace, stability and prosperity in the Asia-Pacific region, and frank and candid discussions of differences,'' the statement said.
White House spokesman Tony Snow told reporters that the Vietnamese leaders expressed hope to ''build closer ties...that not only involve the economy but also security and cultural exchanges.''
Manh was quoted as saying that the two nations should ''put aside the past and look forward to the future.''
Bush conveyed his ''determination'' to have the U.S. Congress pass the bill on permanent trade relations status, which is vital for Vietnam's accession to the World Trade Organization, Snow said.
Snow said Bush stressed the need for Vietnam to promote economic, political and religious freedom, and improve its human rights situation.
Ahead of Bush's visit, the U.S. State Department removed Vietnam this week from a list of ''countries of particular concern'' regarding religious freedoms.
Bush will attend an annual summit here Saturday and Sunday of the Asia-Pacific Economic Cooperation forum and will then travel to Ho Chi Minh City.
The visit is the second leg of his three-nation Asia tour, which has already taken Bush to Singapore and will end in Indonesia.