The action sent the measure to President Bush, who has adopted the agreement negotiated by the Clinton administration as part of his trade agenda.
The U.S. House approved the Vietnam trade agreement in September.
Under the agreement, Vietnam would benefit from the same low tariffs the United States sets for its other trading partners. In return, Vietnam is to reduce its tariffs, eliminate nontariff barriers, protect intellectual property rights and open its markets to American service and investment companies.
The United States and Vietnam had no formal relations and limited contacts in the two decades after U.S. troops left Vietnam in 1973. The first President Bush initiated cooperation in such areas as accounting for MIAs.
In 1994, President Clinton lifted the trade embargo and the next year he established diplomatic relations. In 1998, he issued the first waiver making commercial deals with Vietnam eligible for U.S. government loans and credit guarantees.
But Vietnam has remained one of only six nations denied normal trade relations, subjecting Vietnamese goods to far higher tariffs. The other countries are Afghanistan, Cuba, North Korea, Laos and Yugoslavia.
Vietnam is the world's 14th-most-populous nation, with 80 million people, but trade with the United States was only about $1.2 billion last year. Estimates are that Vietnam's exports to the United States, mainly shrimp, coffee and light manufactured goods, could more than double with normal trade relations.
The vote on Vietnam followed congressional approval last month of a free-trade pact with Jordan. Sen. Charles Grassley, top Republican on the Finance Committee, said he hoped the Vietnam vote would give momentum to efforts to pass a bill this year giving the president authority to negotiate new multinational trade agreements.
Opposition to the deal came mainly from lawmakers who asserted that Vietnam has not fully cooperated in accounting for soliders missing in action (MIAs) from the Vietnam War and should not be entitled to normal trade because of its poor human rights record.
Concerns were also raised by Mississippi Delta senators, who said the agreement lacked protections for the catfish industry. Vietnamese imports, said Sen. Tim Hutchinson are "absolutely destroying our domestic catfish industry."
Leading the effort to normalize ties with Vietnam were three senators who served in the Vietnam War: Sens. John Kerry, Chuck Hagel, and John McCain, a former prisoner of war.
Vietnam's prime minister, Phan Van Khai, initiated the ratification process in Vietnam by sending the trade agreement to President Tran Duc Long.
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