Soviet schoolgirl Katerina Lycheva left her home a week ago for a good-will visit to the United States, so yesterday when a group of schoolchildren began performing a Russian folk dance for her, she instantly leaped off an auditorium stage to join them.

For several minutes she delighted students and teachers at Wheatley Elementary School in Northeast Washington as she swirled around the dancers, who were dressed in colorful long skirts, loose blouses and head scarves.

Katerina, 11, is visiting the U.S. in memory of Samantha Smith, a young American girl who visited Russia in 1983 to further world peace and died last year in a plane crash. Katerina's visit to the school was the first stop on a two-day visit to Washington. Later in the day she met with with Mayor Marion Barry, and last night she went to the circus.

Washington is the third city of a five-city tour that started in Chicago on March 21. A California-based organization, Children as the Peacemakers, is sponsoring the trip.

Katrina Cousar, 11, who led the Wheatley students in the folk dance, said later that she was excited about Katerina joining them. "She is a very good dancer," she said. "I liked the way she moved her arms and turned around."

Katerina had told the packed audience jammed into the school's auditorium, "I am glad you wanted to see me and made me so welcome," and then spoke of her mission for peace in English and Russian, often looking to her translator for assistance.

After presenting the school with gifts of poems, pictures and cutout paper doves signed by Russian students, Katerina launched into an enthusiastic description of orchards planted in memory of the 20 million Russians who died in World War II.

"I could go on and on," she said after a five-minute speech on trees planted as symbols of peace. "I wish everyone in this country would plant trees like that. Why don't you start right away so you can send me pictures of your trees," she said.

The school, at Montello Avenue and Neal Street NE, was decorated with red, blue and white balloons and posters in English greeting Katerina.

Wheatley, a red brick school with heavy grates across the classroom windows, sits in the middle of Trinidad, a small, quiet community of modest brick row houses where the average income is $9,000 a year. Half of Wheatley's students are eligible for free lunches.

The school recently won the D.C. school system's best attendance award for 1984-1985 and has improved its test scores in recent years.

It was the first chance many of the students had had to meet a foreigner. Nancy Yim, 12, stood by the auditorium door handing out programs. "This is very exciting," she said. "This is the first time I've met a girl from another country."

During a brief press conference after the school assembly, Katerina answered questions in Russian, saying through her translator that she was too tired to speak in English. However, she spoke in English when asked by 9-year-old Amy Rose Taylor of a Northfield, N.J., newspaper called the Good News, how American children differed from Soviet children.

"Soviet children are just the same," she said, leaning forward in her chair. "We like cookies and we like to eat. And the girls play with dolls and the boys play with cars."