Mr. Bush made the announcement as he met with Vietnam's visiting prime minister at the White House. It's the first visit by a Vietnamese leader to the U.S. since the end of the war there 30 years ago.
Mr. Bush also praised the communist nation's economic progress, steps toward religious freedom and continued efforts to find the remains of U.S. troops who died in the Vietnam War.
The two leaders talked about Vietnam's desire to join the World Trade Organization, business issues, human rights and signed an agreement that the president said would make it easier for people to worship freely in Vietnam.
"I want to thank the prime minister for his government's willingness to continue to work on finding the remains of those who lost their lives in Vietnam," said Mr. Bush. "It's very comforting to many families here in America to understand that the government is providing information to help close a sad chapter in their lives."
As the 71-year-old Vietnamese leader met with Mr. Bush in the Oval Office, several hundred protesters outside demonstrated against repressive conditions in the communist nation.
CBS News Correspondent Peter Maer reports that protesters carrying signs reading, "Khai is a terrorist" pressed against the White House fence as the meeting took place. They said their complaints included government violation of human rights.
Khai said: "We believe that America can find in Vietnam a potential cooperation partner. We have a population of 80 million people, which means a huge market for American businesses. And these people also very hardworking, creative and dynamic. And they are now working very hard to achieve the goal of building Vietnam into a strong country with wealthy people and a democratic and advanced society."
He said although there were cultural and historic differences between the United States and Vietnam he and Mr. Bush agreed the two nations could work together to reduce differences and improve bilateral relations.
Khai's talk with Mr. Bush is part of a weeklong visit to the United States where he is meeting with business leaders on both coasts. Khai is ringing the opening bell at the New York Stock Exchange later this week — evidence of Vietnam's economic gains over the years.
"The United States strongly supports Vietnam's integration into the world economic community and its bid to join the World Trade Organization," White House press secretary Scott McClellan said Monday. "They will also use this as an opportunity to work to address religious freedom and human rights concerns."
After his discussions with Mr. Bush, Khai planned to meet with Defense Secretary Donald H. Rumsfeld. Military ties between the two countries have included periodic docking of U.S. warships in Vietnam and plans for U.S. military training of Vietnamese officers. Intelligence sharing and cooperation on counterterrorism activities also are part of the mix.
Also Tuesday, officials from the two countries will sign an agreement at the State Department to cooperate on adoptions.