The private health center that began dispensing free birth control devices and information in Alexandria two weeks ago announced last night that it plans to open two more clinics, near high schools in Fairfax and Arlington counties.

Gail Frances, president of the Annandale Women's Center, had already announced plans to open a free clinic near T.C. Williams High School in Alexandria to make birth control devices, physical examinations and counseling more accessible to teen-agers. The clinics announced last night would be opened near Woodson High in Fairfax and Wakefield High in Arlington by September.

Since April 15, the center has offered birth control services free to students at its office at 2817 Duke St. near Alexandria's King Street Metrorail station. The number of teen-agers going to the center has doubled in that time to two dozen a week, Frances said.

The plans to open more centers to serve teen-agers got a mixed reaction last night from Fairfax, Arlington and Alexandria officials.

"We certainly wouldn't encourage them," said Fairfax County School Board Chairman Mary E. Collier. "I don't believe that's what this community wants." Collier said the School Board will not try to stop the Annandale Women's Center's efforts because the center is a private undertaking, but she said the board likely would not support the center's plans.

Arlington School Board Chairman Gail Nuckols said the proposed Arlington clinic will stir controversy. "There will be people strongly against it and for it," she said.

Alexandria Mayor James P. Moran Jr. said he supported the group, adding that "it provides an important service that Alexandria is obviously in need of."

Frances, who announced the plans for the new centers at a reception at the Alexandria Community Y, said, "I know there is concern that we are undermining the family . . . . We are doing this because we've been in the business for 13 years and the abortion rate and the pregnancy rate has gone nowhere but up."

In 1984, there were 1,537 reported teen-age pregnancies in Fairfax County, 350 in Alexandria and 301 in Arlington, according to the Virginia Center for Health Statistics.

The Catholic Diocese of Arlington, the Falls Church-based Committee to Protect the Family and many parents oppose the free clinics, saying the solution to curbing early pregnancies lies in teaching students to say "no."

Planned Parenthood, a group that offers birth control devices and other health services to teen-agers, has endorsed the Annandale Women's Center's efforts. Rosann Wisman, executive director of Planned Parenthood, said yesterday that clinics on school grounds would be even more successful in preventing unwanted pregnancies.

This month, the Alexandria School Board rejected a request that the school system operate a birth control clinic at T.C. Williams High.