Secretary of State Alexander M. Haig dropped in at the Egyptian Embassy yesterday morning for coffee with Jihan Sadat, wife of Egyptian President Anwar Sadat. It was Sadat's first event on an itinerary that included tours of four museums, lunch at the White House, an afternoon reception at the District Building and the keynote address at the National Academy of Sciences to officially open the "Egypt Today" cultural exhibition.

"It was very, very nice of him," said Sadat of Haig's appearances. "He told me he was coming to Cairo and he was looking forward to seeing my husband there."

Among those at the half-hour gathering were Egyptian Ambassador Ashraf Ghorbal, Betty Atherton, wife of U.S. ambassador to Egypt Alfred Atherton, and Nicholas A. Veliotes, the State Department's assistant secretary for Near Eastern and South Asian affairs.

As the group finished its coffee, Tom Lawton, the director of the Freer Gallery of Art, and John Pope, director emeritus, were standing outside the Freer in their gray suits awaiting Sadat. Around them stood Janet Solinger, director of the Smithsonian's Resident Associate Program; John Jova, president of Meridian House Internatinal; and Dean Brown, head of the Middle East Institute. All three organizatons are sponsors of "Egypt Today." Meridian House, which has mounted an exhibit of Egyptian costumes, rugs and basketry, hosted a luncheon for Sadat on Sunday.

"I'm a Chinese specialist," said Lawton, "except today when I'm an Egyptian specialist for 15 minutes."

It was more like five. Jihan Sadat arrived in mauve-colored suit, her hair pulled back, her eyes ringed with kohl , the black liner that Egyptian women use. Lawton escorted Sadat and the accompanying entourage past a number of displays and then down the street to the Smithsonian Castle where Smithsonian Secretary S. Dillon Ripley and his wife, Mary, waited. Lawton bowed, shook Sadat's hand, and gallantly swept a hand out toward Ripley, who took over the tour.

Sadat thanked Ripley "for all of your work, for your timeless spirit," and the group moved on to the ancient Egyptian art, housed in a dark, carpeted room with thick, lush plants. "These are canopic jars made of alabaster," said Ripley in front of one glass case, "for preserving the innards before mummification."

"The best alabaster comes from Beni-Suef," said Sadat of her home town.

"The intestines would go in one canopic jar, the stomach in another," Atherton said, "for reassembling in the afterlife."

Suddenly a waiter appeared with stacks of china saucers and cups, a bowl of sugar cubes. "Ah, the coffee," someone said.

The party proceeded to the Hirshhorn, where director Abram Lerner took Sadat and the ever-growing entourage through the exhibit of work by Egyptian sculptor Mahmoud Moukhtar, pausing at his small granite called "Seated Woman."

"The women don't sit very much because they're all very busy," Sadat said. Everyone laughed. She said: "I must thank Mr. Hirshhorn for his beautiful museum, thank him for giving us an opportunity to have some of our sculpture in his lovely museum. We are happy to show you some of our modern arts."

On the third floor, Lerner showed Sadat some of the Hirshhorn's modern art. She glanced back at a Max Beckmann sculpture of a man holding a tiny woman in his hands.

"Adam and Eve," said Lerner.

"Yes," Sadat said, smiling.

She walked through the rain to the limousine waiting to take her to the Museum of American History's exhibit of Egyptian jewelry, decorative arts and pictures of American architecture influenced by Egyptian designs.

Asked for more remarks, Sadat said, "I'm afraid I'm going to repeat what I've been saying. I hope you're not fed up with me. You are the most powerful of countries in the world, but you still need to exchange ideas and culture with developing countries like us, and both can develop."

After lunch, Sadat wne to the District Building where she was greeted by about two hundred people mobbing the hallway outside Mayor Barry's office.

"I feel a particular kinship to Egypt," said Mayor Barry to the sound of laughter. "I was born in Tennessee in Memphis. There's a Memphis in Egypt too."

Marion Christopher Barry, the Barrys' infant son, was brought out by father and mother for some cuddling with Sadat. As Cameras clicked and the crowds moved closer, the baby couldn't handle it and began crying. He was handed over to a godmother.

But Sadat, who appears to have an enormous tolerance for these events, posed for still more photos, and made still more remarks; "I feel the warmth of the American people. You have captured my heart." She left smiling.