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.
In the 10 years since diplomatic ties were restored after the Vietnam War, the United States has become Vietnam's top trading partner. Last year, two-way trade was worth $6.4 billion.
Sen. John McCain, R-Ariz., a former Navy pilot imprisoned for nearly six years in Vietnam after his plane was shot down during the Vietnam War, said Tuesday that Vietnam had made sufficient economic progress to warrant inclusion in the WTO. But, he added, the United States expects progress in other areas, such as human rights.
"We have every right to expect the Vietnamese to make significant improvements in human rights and religious freedom," McCain said on NBC's "Today" show. "They have taken some steps. ...Our message throughout the world is that we expect progress toward democratic freedom, human rights, elections and all the trappings of democracy."
After he arrived in the United States on Sunday, the Vietnamese leader stopped at Boeing Co.'s plant south of Seattle to oversee the purchase of four 787 airliners by Vietnam Airlines.
On Monday, Khai met with Microsoft Corp. Chairman Bill Gates at the company's headquarters in Redmond, Wash. The two announced that they had signed two memoranda of understanding, to train and develop more Vietnamese information technology companies and to offer computer and software training to more than 50,000 teachers.
While Khai will want to talk about business, Mr. Bush is being pressured by human rights groups and some members of Congress to link any trade concessions with improvements in Vietnam's human rights record. "There are some steps that have been taken by Vietnam, but there are concerns that remain," McClellan said.
The U.S.-based Human Rights Watch says it has documented cases of abuses by the communist government, including the arrests of dissidents for promoting democracy or human rights. In Seattle, Khai was greeted by demonstrators who shouted "Down with communists!" and called for an end to political and religious persecution.
During Sunday's demonstration, Nhien Le, a former officer in the South Vietnamese Air Force, said his fellow demonstrators hoped their presence would let Khai know that Vietnamese Americans want him to address human-rights abuses in Vietnam.
The president and Khai also are expected to deepen joint efforts to achieve the fullest possible accounting for Americans who remain missing from the Vietnam War. Veterans groups and families of servicemen still missing in Indochina criticized the Republican-controlled Congress back in 1995 when President Clinton took steps to restoring relations between the once bitter enemies.
Khai's visit this week has not prompted any of that opposition, in part because Vietnam is cooperating in the search for U.S. service members.