President Reagan, cheered by recent polls that show his approval rating among blacks at record high levels, yesterday launched a week-long campaign designed to give visible recognition to the late Rev. Martin Luther King Jr. and other leaders of the civil rights movement.

The events, including a speech Wednesday at Martin Luther King Jr. Elementary School here, are timed to coincide with the 57th anniversary of King's birth, a national holiday -- to be observed Monday -- that Reagan once opposed.

White House political assistant Mitchell E. Daniels Jr. called the president's recent gains among blacks "a very welcome development" but said this week's events were planned before recent polls showed Reagan gaining in black support.

A CBS-New York Times poll this month gave Reagan a 56 percent approval rating among blacks, far higher than he has received in the past. Daniels said this probably exaggerated the president's support and observed that recent surveys by Republican pollsters Robert Teeter and Richard Wirthlin gave Reagan approval ratings of 36 percent and 38 percent, respectively, among blacks. The latest Washington Post-ABC poll also gave Reagan a 36 percent approval rating.

Even the 36 percent figure is a marked improvement for Reagan, whose approval rating among blacks in the early years of his presidency was usually well below 20 percent. The president received 11 percent of the black vote in 1984.

Daniels attributed Reagan's gains among blacks to a variety of factors, including "economic growth, the absence of controversial issues since the election and, to some extent, the perception that the president is committed to peace" in the wake of the Geneva summit. Wirthlin gave a similar account and said that "blacks recognize more than other voters that Reagan's tax-reform proposal is positive for them."

A White House official who asked not to be identified said Reagan was "gratified" with the surveys because he had "always been bothered" by his low popularity in the black community. Throughout his political career, Reagan has bridled at suggestions that he was prejudiced against blacks, and he has sometimes been critical of black leaders for statements he said fostered this impression.

Reagan met yesterday with the Council for a Black Economic Agenda, a group of economists and business people who share the president's view that private enterprise is the most successful path to black advancement. On Thursday he will present a posthumous award to Roy Wilkins, the former head of the NAACP and on Friday meet with King's widow, Coretta Scott King.

During the controversy over making King's birth a national holiday, Coretta King charged that the president "doesn't represent America." But when political pressure mounted in 1983 in behalf of the King observance, Reagan reversed himself and signed legislation making the birthday a federal holiday. It will be observed nationally for the first time Monday.