Washington Hospital Center yesterday became the second area hospital to seek health planning approval to begin transplanting human hearts.

Its application pits the hospital center against Fairfax Hospital, another center of cardiac surgery in metropolitan Washington that wants to open a heart transplant unit.

The project review committee of the Northern Vrginia Health Systems Agency voted last night 4 to 0 with one member abstaining to deny Fairfax Hospital's request for a heart transplant center. The health planning agency's full board will vote on the project on Monday.

The two hospitals' requests represent the growing popularity and success of heart transplants, which only three years ago were considered too experimental to be covered by most health insurance plans.

In an application filed with the District's State Health Planning and Development Agency, Washington Hospital Center said it could begin the service after a $10,000 renovation of one patient room.

Although the current request covers only live heart transplants, hospital officials said they will consider expanding the program to include mechanical hearts "once the technology is further developed."

Washington Hospital Center, the District's largest, currently operates a kidney transplant center, skin bank, tissue-typing lab and organ procurement center, as well as performing the largest volume of heart surgery in the region. It performed more than 1,300 open heart surgeries in 1985, about twice as many as Fairfax Hospital.

Under health planning laws, each jurisdiction issues its own approval for new hospital services and equipment. Duplication of services within regions should be considered, according to health guidelines.

Dr. Carlessia Hussein, director of the District planning agency, said an advisory group is planning to issue guidelines on what heart transplant services are needed in the Washington area. The group, the Metropolitan Health Planning Council, probably will take six months to write the guidelines, she said. But the Virginia and District health planning agencies are free to approve centers before the council acts, she said.

A U.S. task force on organ transplantation has recommended that new heart transplant centers be approved only at hospitals that already operate some type of transplant program, in order to reduce duplicating tissue-typing labs and experts in organ rejection techniques.

"We already do heart surgery on a regional basis and are not limited to just one side of the river," said Stephanie McNeil, a spokeswoman for Washington Hospital Center.

Fairfax Hospital officials have said that Georgetown University Hospital, which operates a kidney transplant program, will provide tissue typing and other services that the Virginia hospital does not have.

Washington Hospital Center, in its application, said there are enough patients and donor hearts to support a program in metropolitan Washington. It estimated that 10 to 20 people in the area received heart transplants last year at other hospitals.