A private Alexandria health center announced yesterday that it will dispense free birth control devices to all Northern Virginia high school students who request them, beginning April 15.

The Annandale Women's Center, a state-regulated facility with four registered nurses and three affiliated physicians, decided to bear the costs because local governments and school systems have shied away from the issue, said Gail Frances, president of the center.

Located at 2817 Duke St., the center will give female and male students a full range of reproductive services without charge, including pelvic examinations, treatment for sexually transmitted diseases, pregnancy testing, counseling and birth control information.

To make the free services even more accessible, the center plans to open an additional comprehensive health clinic near T.C. Williams High School in the fall.

"The nurses and I have seen an escalation in the number of teen-age pregnancies in Northern Virginia," said Frances. "Part of the problem is accessibility, transportation problems, and the reluctance to go to public health clinics."

In 1983, 360 Alexandria unwed teen-agers were reported to have become pregnant, the highest percentage in Northern Virginia, according to state health statistics.

Religious leaders said they opposed the center, which also performs abortions. Parents and school officials said they were concerned by the center's offer.

"We are against it," said Ellen McCloskey, spokeswoman for the Catholic Diocese of Arlington. "By this we are condoning premarital sex for young people who are not prepared, not mature enough to handle it.

"Monetarily, what do they have to lose? Morally they have a lot to lose."

McCloskey said the diocese will ask parents, elected officials and some of its 205,000 members to protest the health center's offer.

Lawrence W. Gladieux, PTA president for T.C. Williams, said his chief concern is that the center will not require parental permission for any of the services.

"If they dispense them without parents' consent, there will be some strong opposition," he predicted.

School Board Chairman Lou Cook said she would disapprove of the clinic if it were on school property because "we are hard pressed to find space to conduct classes in." Because it will be on private property, she said, "what they do is their business."

Frances, the founder of the Northern Virginia Women's Medical Center in Fairfax, Virginia's first abortion clinic not affiliated with a hospital, is familiar with protests. After the Fairfax center began performing abortions in 1973, numerous demonstrations and arrests took place outside it.

Rosann Wisman, executive director of Planned Parenthood, a group that offers health services and birth control counseling on a sliding payment scale to about 18,000 patients a year in seven Washington area clinics, said there is a great need for health care for teen-agers.

She said school-based clinics are "popping up all over the country," and that she hoped the one in Alexandria would include more than just sex-related services.