In a strong bipartisan vote intended to make it easier for President Clinton to end decades of rancor with a former enemy, the Senate voted today to urge that the trade embargo against Vietnam be lifted soon. The White House had supported the measure behind the scenes.

After an emotionally charged debate about the lessons of the Vietnam War and the fate of missing servicemen, the Senate, by a 62-to-38 vote, agreed with the bill's chief sponsor, John F. Kerry, a Massachusetts Democrat and Vietnam veteran, who said it was time "to put the war behind us."

Although the resolution is not binding, Administration officials said today that it would certainly make it easier for Mr. Clinton to take the politically sensitive step of ending the 19-year embargo, closing a chapter on a war in which 58,135 Americans died. 'A Seminal Event'

"The vote will give the President the kind of political cover he needs to lift the embargo, and I expect that relatively soon," said Senator John McCain, an Arizona Republican and a sponsor of the bill, who was a prisoner of war in North Vietnam for five and a half years. "I think it's a seminal event in U.S.-Vietnamese relations."

A consensus emerged among senior Administration officials last month to lift the embargo, but they decided that action would be put off to take political soundings around the country and determine how much backlash there would be. Administration officials acknowledge that this is a particularly sensitive issue for Mr. Clinton because he, like thousands of Americans in his generation, avoided military service during the Vietnam War. 2,200 Americans Missing

Today's resolution aimed to show the President that lifting the embargo has widespread political support and is not a betrayal, as some veterans groups argue, of servicemen missing in Vietnam. Forty-two Democrats and 20 Republicans voted to lift the embargo; 14 Democrats and 24 Republicans voted against.

Last summer, President Clinton indicated he would lift the embargo if Vietnam cooperated in providing the fullest possible accounting for the more than 2,200 Americans missing in Indochina.

Now, the question in the Administration is not whether the embargo will be lifted, but how soon, though some officials say the President needs to do some more explaining to veterans' groups and families of missing servicemen.

The White House regarded the vote as useful in calling attention to the progress that Vietnam has made in meeting the conditions set by the Administration, officials said. But they said they did not expect Mr. Clinton to follow the Senate recommendation immediately.

Dee Dee Myers, the White House spokeswoman, said, "We certainly welcome the Senate's sentiment." But she said the Administration was still considering whether Vietnam had made sufficient progress toward providing information about P.O.W.'s and M.I.A.'s and on other fronts for full relations to be restored.

Many veterans' groups and family groups opposed today's resolution, arguing that Vietnam has not done enough to resolve the cases of missing Americans. American Legion Opposes Move

"The American Legion is both disappointed and concerned," said John F. Sommer Jr., the executive director. "However we are not going to give up the fight. Vietnam has not cooperated by a long shot."

Defying the intense lobbying by these groups, the Senate approved a resolution that said Vietnam's cooperation has increased significantly over the last three years in resolving the cases of missing Americans. The resolution also noted that senior American military officials feel that lifting the embargo will accelerate efforts to account for prisoners or war and missing servicemen.

Republicans in the Senate split almost evenly on the vote, with some convinced that Vietnam was making strenuous efforts to provide information on missing servicemen. Other Republicans appeared ready to use lifting the embargo as political ammunition against the Democrats. Complaints From Businesses

Many companies have quietly told Republicans and Democrats that the embargo is hurting American business as Vietnam opens its economy to the outside world.