"It's very nice to be back, actually," said the princess, emphasizing the "actually" the way the English do. Her Royal Highness Princess Anne of Britain was at the District Building when she said it yesterday, receiving the keys to the city.

It was the first full day of her five-day visit to the United States, one planned some months ago so that she can dedicate a statue of her royal ancestor and namesake Queen Anne on Saturday at Centreville on the Eastern Shore Of Maryland.

The remark was like a wave of a royal wand, sweeping away with one flick any impressions she had left behind in 1970 when her behavior as a bored, petulant princess visibly annoyed with duty, press and the No. 2 spot raised a few well-placed eye-brows.

Then she was 19 and travelling in the shadow of her older brother, Prince Charles. Yesterday she was very much the princess royal, gracious, smiling and obviously enjoying duty and spotlight as No. 1 as she made up her arounds of city hall, the Smithsonian and the White House.She met President Carter in the Oval Office and Rosalynn Carter in the Yellow Room.

Only once did she suggest any lingering qualms she might still have of American press as she and her husband, Mark Phillips, arrived at the White House to meet Chip and Caron Carter, their hosts for lunch. Chip told her that photographers wanted them to pause for pictures before they went upstairs.

"They're very original, aren't they?" the princess said.

Her day was jammed with events long before she ever got to the British embassy garden party to close the day. She was what the British might call "sensibly" dressed - wearing a blue and white maternity dress, (she is four-months pregnant) brimmed, blue straw hat with flowers around the crown white gloves, white handbag and shoes.

Onlookers were scarce as she and Philips arrived at the District Building, Stepping out of a gleaming blue embassy Daimler to be met by Major and Mrs. Walter Washington.

Her mother, Queen Elizabeth II, had been the "first reigning queen" to visit city hall when she stopped a year ago on her Bicentennial tour, Washington told the princess.

"Really , you don't get too many of them then?" she replied, an observation that speaks as much for the detachment with which rolyalty views its own as it does for the dwindling numbers of royal visitors.

Upstairs, standing beside the mayor and smiling, she faced a battery of photographers. She was "very honored" and "very touched" to receive the city's keys. Her mother had enjoyed her visit - "You kept her very busy."

Benetta Washington, taking her turn, hailed the princess as "a model for all the youngsters" - 20 Washington artists whose works were on exhibit, Youth Symphony Orchestra members and others gathered for the ceremony. Their gift to her: a cameo in crystal of Elizabeth I.

Third in line but empty-handed was D. C. Council chairman Sterling Tucker who said he said he had "nothing to give except love and affection of us all . . . and a great deal of affection for your people."

Anne's one attempt at levity came when she presented a framed photograph of her and her husband. "You no doubt have a formidable rogue's gallery by now," she told the mayor, "but on behalf of Capt. Phillips and myself I'd like to make an additon." It made his collection of the royal house of Windsor complete, Washington said.

Later, skipping the cheese, crackers, wine and fruit, Anne made a point of asking to meet some of the artists whose works are displayed outside the mayor's office as part of Gallery 2, a permanent exhibit of lesser-known Washington artists.

"She was utterly charming, very tender, warm and loving," said Barbara Fiedler, who set up the exhibit as she had a similar one last year for the queen's visit.

At the Smithsonian's Museum of History and Technology, where she was met by S. Dillon Ripley, Anne and her husband also were met by the first crowds of the day. She acknowledge their applause with a royal glance, given first to the right, then to the left.

Inside at the "Silver Jubilee" exhibit, mounted in commemoration of her mother's 25 years on the throne, she saw what probably was some familiar-looking memorabilia. It belonged to her mother's own collections and was on loan from Buckingham Palace and Windsor Castle.

In the "We, the People" exhibit upstairs. Margaret Klapthor, political history curator, gave her a quick course in American history, commencing with the westward movement of pioneers by wagon trains.

"It was not very pleasant," the princess noted, hearing of the hardships.

The reproduction of a log cabin prompted Ripley to point out its importance in the origins of American Presidents.

"They have to be born in a log cabin," said Ripley.

"Even now?" the princess asked.

"It helps," Ripley replied."