NEW YORK (AP) _ Soviet ''peacemaker'' Katerina Lycheva arrived in the nation's largest city Sunday, saying that adults often find it difficult to agree but that ''if it was up to the children, it would take us about a minute or so to get together.''

The 11-year-old Katerina arrived from Chicago arm-in-arm with her traveling companion Star Rowe of San Francisco.

Each girl lighted a candle after arriving at LaGuardia Airport.

''I light this candle and I hope the sun will always shine as bright as this candle,'' Katerina said. ''And I think that it will shine to all children in the world, and for this we must struggle for peace.''

Star said, ''I light this candle because if we don't have peace in the world, we have no world.''

Speaking to reporters, Katerina said: ''Sometimes grown-ups find it very hard to get together to agree about things. They quarrel, they fight. I think if it was up to the children, it would take us about a minute or so to get together.''

Katerina's two-week, five-city tour - her first trip outside the Soviet Union - is sponsored by the San Franciso-based Children As The Peacemakers. It was prompted by a 1983 Soviet tour by Maine schoolgirl Samantha Smith, who died in a plane crash last year.

On Monday, Katerina was scheduled to be interviewed on two national television programs, participate in an exchange of ''peace letters'' at a Brooklyn public elementary school and go sightseeing.

She said she looked forward most to seeing the Statue of Liberty.

In Chicago, an American family welcomed Katerina into their home Saturday night, where she sampled barbecued chicken, toyed with a computer and made friends with children oblivious to their nations' differences.

''It was just like having a friend over,'' said 11-year-old Kristy Mace of suburban Oak Park. ''She was shy at first, but then she loosened up. We talked about what anyone would talk about if you didn't know each other.''

Kristy's parents, Stuart and Katherine Mace, were chosen to play host to Katerina as members of the International Visitors Center, which helped coordinate the girl's 2 1/2 -day stay in Chicago.

The Maces greeted their visitor with a hand-painted sign in Russian that read, ''Welcome Katerina.'' They also presented her with a gift-wrapped box containing 127 peace letters from pupils at Abraham Lincoln Elementary School in Oak Park, where Kristy goes to school. The letters are for Katerina's Moscow classmates.

The Maces served a home-cooked meal of barbecued chicken, potato salad and Jell-O. After dinner, Katerina and Star played with Kristy and her brother Michael, 15, who showed her how to use the family computer.

Mrs. Mace said the visit had ''a light, friendly atmosphere,'' but added, ''I think it had a profound meaning.''

''I think that one-to-one diplomacy and personal contact are the things that will make the difference'' in easing relations between the United States and Soviet Union, she said.

The rest of her trip will take her to Washington, D.C., on Wednesday and Thursday; Houston, March 28-30; and Los Angeles, March 31-April 1.

Pat Montandon, founder of Children As The Peacemakers, said she came up with the idea of having a Soviet child make a peace mission to the United States after the group gave a posthumous award to Samantha Smith last November.

Star, the daughter of a San Francisco street artist, won an essay contest sponsored by the group to select a traveling companion for Katerina, Ms. Montandon said.

Katerina left her Moscow home with her mother, a research scientist, last week and arrived Thursday night in Chicago. Her father is a specialist in commercial advertising.

A fifth-grader at Moscow's English Speaking School No. 4, Katerina was chosen for the tour by her colleagues in the ''Club of International Friendship of Moscow.''