The House voted 338 to 90 yesterday to create a new national holiday in memory of the Rev. Martin Luther King Jr.

Bills to declare such a holiday have been introduced every year since King was assassinated in 1968, and, until yesterday, the House always shunted them aside. This time, overriding scattered and mainly Republican objections, it agreed overwhelmingly to set aside the third Monday every January in his honor, the 10th such holiday in the federal code. The bill goes to the Senate, where its future is cloudy.

In Georgia, King's widow, Coretta Scott King, said she was "pleased and encouraged" by the House action. "I hope the Senate will move as swiftly and responsibly," she told United Press International.

In the House yesterday Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.) concluded a parade of praise for the slain civil rights leader by recalling King's famous "I Have a Dream" speech at the Lincoln Memorial here 20 years ago.

O'Neill recalled that he and other members of Congress were there despite the efforts of some "small men in the Congress" to force them back to Capitol Hill with a series of unnecessary quorum calls and roll calls.

"As I sat there in the sweltering August sun, I watched a great man change the course of history," O'Neill said. "Martin Luther King changed America--all of America. He changed it not by force of arms, but by moral force. He asked us to become the country that we always claimed to be: a country of equal justice, of equal opportunity, a country where all men--all men--are created equal."

Rep. Jack Kemp (R-N.Y.) said he had once resisted the idea of a holiday for King but had changed his mind, having coming to believe "that the American Revolution will not be complete until we complete the civil rights revolution." Kemp said he wanted to see his Republican Party stand for that proposition and that he wished that the vote could have been unanimous.

The Reagan administration, however, opposed the measure on grounds that King could be commemorated more inexpensively without requiring another paid holiday for federal employes.

Rep. William E. Dannemeyer (R-Calif.) led the opposition on that score, contending that King, who was born Jan. 15, 1929, ought to be honored on a Sunday. He called King a man who "stood for jobs and work," and argued that "a paid holiday for federal workers is the wrong statement at the wrong time."

"What do you mean, 'cost'?" Rep. Parren J. Mitchell (D-Md.) demanded in reply. "What was the cost of keeping things the way they were?"

House GOP ranks were closely divided in the vote that followed. Eighty-nine Republicans joined 249 Democrats in voting for the holiday. Seventy-seven Republicans and 13 Democrats voted nay.

The House voted in December, 1979, to commemorate King on a Sunday, a step that led at the time to the bill's withdrawal. Under the measure approved yesterday, the new holiday would go into effect in the first January two years after enactment. The Congressional Budget Office estimated an annual expense of $18 million a year.

A Washington Post-ABC News poll earlier this year indicated that the American public was evenly divided on the question of a holiday in King's honor. Forty-seven percent said they thought there should be one and 47 percent said there should not. Five percent had no opinion. The only other American honored by a legal public holiday is its first president, George Washington.

In the Senate, the bill will come under the jurisdiction of the Judiciary Committee. It is not expected to move quickly there.