Virginia hospitals, faced with critical staffing shortages that could prompt cutbacks in services, started a statewide educational and public relations campaign yesterday that they hope will reverse a decline in the numbers of young people entering the nursing profession.

At news conferences at Arlington Hospital and throughout the state, the Virginia Hospital Association announced a yearlong program that will feature billboard, newspaper and magazine public service announcements, a toll-free telephone number for information on nursing, and other educational activities.

"The misconception is that nurses are leaving the profession. The truth is that not enough people are becoming nurses to meet growing health care needs," said T. Carter Melton, chairman of the hospital association.

The initiative announced yesterday is one of Virginia's responses to a growing national health care problem. At the end of 1986, 13.6 percent of registered nurse positions at U.S. hospitals were unfilled, double the vacancy rate of a year before.

Virginia hospital officials say the extent of the state's nursing shortage is unknown, but officials at several Northern Virginia facilities have reported vacancy rates ranging from 5 to 12 percent, and have said that the needs at some rural hospitals in the state are even greater.

D.C. Hospital Association officials estimated that the nurse vacancy rate in Washington is 15 percent. Rick Wade of Maryland's hospital association said most hospitals in that state have nursing vacancy rates of 11 to 13 percent.

Although there have been nursing shortages in the past, most recently in the late 1970s, Virginia officials said the current situation is particularly alarming because, for the first time, nursing schools are reporting steep declines in numbers of applicants while the demand for nurses is increasing.

Between 1983 and 1986, Virginia's nursing schools reported a 21.2 percent decline in admissions, from 2,880 to 2,268 enrollees. At the University of Virginia nursing school, the number of students enrolled in the undergraduate program has decreased from 309 to 187 since 1985.

"We're not getting a strong interest in nursing," said Betty M. Johnson, associate dean of the U-Va. nursing school, one of the state's largest. "The salary is not that high and it caps off . . . . There are a lot more competitive majors for women. People have a lot more options."

As one way of increasing the applicant pool, Johnson said, the school recently decided to allow freshmen to enter the nursing school directly, instead of waiting until their junior year. But she and other health care officials said hospitals must increase salaries and the prestige of nursing to persuade people to make nursing a career.

"It is not enough to say they appreciate us," said Meg Lay, a nurse who works part time in the psychiatric department at Arlington Hospital. "The appreciation has to be less condescension" and improved salaries and involvement in decision-making, she said.

Priscilla Jobe Shuler, vice president for nursing at Mary Washington Hospital in Fredericksburg, said the average salary for starting nurses in the state is roughly $21,500 a year -- less than the national average of about $22,275. However, hospital administrators said that the sellers' market is driving nurses' salaries upward.

John P. Sverha, president of Arlington Hospital, where the nurse vacancy rate is about 8 percent, said the hospital last year raised nurses' salaries 12 percent, followed this year by a 6 percent increase.