Philippine President Ferdinand Marcos, accompanied by a dozen of his Cabinet members and close advisers, arrived in Washington yesterday for a state visit to the United States designed by both governments to demonstrate broad public approval for the longstanding U.S.-Philippines relationship.

Security was tight on the Washington Monument grounds as Marcos and his wife, Imelda, arrived in separate presidential helicopters to be greeted by Secretary of State and Mrs. George P. Shultz.

Several hundred flag-waving members of the Filipino-American community, along with a band, welcomed Marcos as he stepped from the helicopter. Drowned out in the noise were the shouts of a dozen protesters who had been relegated to a small knoll behind a screen of trees, where Marcos was unlikely to have seen them.

Both the welcome and the protest demonstration were temperate in contrast to expectations raised by the elaborate preparations of the Philippine Embassy and the emotional calls for opposition to the Marcos visit by Filipinos in this country who oppose his government.

It is Marcos' first visit to the United States in 16 years, since the first year of his presidency in 1966. His country has been a staunch supporter of the United States throughout his rule, but relations between the two governments became tense during the Carter administration with its emphasis on human rights.

A number of members of Congress have publicly opposed the Marcos visit, charging that his government continues to abuse fundamental rights. But Reagan administration spokesmen have brushed these charges aside, citing a "trend toward normalization" in the country.

Administration spokesmen instead have emphasized the strategic importance of the Southeast Asian nation, which is home to two major U.S. bases, Clark Air Base and Subic Naval Base. They have been a cornerstone of the U.S. defense posture in Asia and have assumed increasing importance with the onset of instability in the Persian Gulf.

Dozens of Marcos aides and Philippine political figures were aboard the separate jets that President and Mrs. Marcos took to the United States. Scores of Filipino journalists preceded them on commercial flights and were well represented yesterday for his arrival, with television carrying the scene back for prime time evening viewing in Manila.

Marcos opponents have charged that he is spending millions of dollars on the U.S. visit to promote his image at home at a time when his country faces international debt problems and a nagging insurgency by anti-government guerrillas. Government officials claim the figure is under a million dollars.

Marcos will be in the United States for almost two weeks and his active schedule includes meetings with government figures, politicians, businessmen, the media and the Filipino communities in Washington, New York, Los Angeles, San Francisco and Honolulu. A large advance team, including four special ambassadors, has been in the country for several weeks preparing for the visit.

President and Mrs. Marcos are to meet with President Reagan following an official White House welcoming ceremony this morning. Mrs. Marcos, 52, governor of Manila and also a member of the Cabinet, is widely mentioned as a possible successor to Marcos, 65.

His other scheduled meetings with officials here before he leaves for New York on Sunday include sessions with Vice President Bush, Shultz, Secretary of Defense Caspar W. Weinberger, the House and Senate leadership and members of the Senate Foreign Relations and House Foreign Affairs committees.

Marcos is expected to press for an early opening of talks on the future of the Clark Field and Subic Bay bases and for action on an extradition treaty that has been negotiated but not yet submitted to the Senate for ratification. The discussions also are expected to lead to a new U.S.-Philippines joint military commission.

The extradition treaty could prove to be a troublesome element in Washington-Manila relations when it is finally submitted, probably early next year, just about the time talks on the bases likely will be getting under way. Senate sources say that the large Filipino community in the United States has mobilized an active campaign against the treaty, raising questions whether it could get the necessary two-thirds vote.

U.S. officials say it is unlikely that human rights questions will come up in the discussions between Marcos and Reagan, and emphasize the "quiet diplomacy" that has become the administration theme on human rights.

"We know there is a problem," a senior administration official said. "It is our policy to discuss these things but with private, diplomatic means. We think we can get more accomplished . . . . "