After two rejections, Doctors Hospital was granted yesterday the city government's approval to continue providing health care in downtown Washington after its present building is torn down in June 1980.

The decision to grant the hospital an extended certificate of need was announced by the city's Board of Appeals and Review. It is based on a settlement reached between the private, profit-making hospital and the District's State Health Planning and Development Agency. The agreement allows the hospital to move ahead with plans for a $19,730,000 renovation of the Metropolitan Hotel, at 1143 New Hampshire Ave. NW, to convert it into a hospital.

"This puts us back in the starting gate," said Dr. Karl Joans, president of the hospital's medical staff. "We don't anticipate any problems now, but we didn't anticipate any" before, he said.

The dispute between the 40-year-old hospital and the city government focused on who would have financial control -- and thus control of the health care -- of the hospital in its new location. The question was whether control would lie in the hands of Washington Medical Center Inc., the hospital's parent corporation, or American Health Services Management Inc., which is to take over the new building and lease it back to the hospital.

The health planning agency turned doen the hospital's request for an extension of the certificate of need -- a document required for a hospital to do any building or expansion -- on the grounds that financial control of the institution would rest with American Health Services Management Inc. instead of the hospital itself.

A denial of the certificate of need would permanently close the facility, at 1815 I St. NW, which supporters contend is an anchor tying hundreds of physicians to the downtown area.

According to Robert Cadeaux, chairman of the three-member board which heard the case last week, the "substantive issue" was whether Doctors Hospital, through it's financial arrangement with American Health Management, had surrendered its control over the quality and cost of medical services.

"I am happy to say the answer to that question is 'no,'" Cadeaux said in a statement released yesterday.

District officials said as part of the "settlement" between the city and the hospital, thd hospital charged its financial arrangements with American Health Management, and agreed to certain conditions that were added to the certificate of need.

Among the conditions are requirements that:

There be a firm schedule of construction submitted to the health planning agency within 30 days.

The settlement of the financial arrangements occur within 15 days of the date the hospital receives its building permits.

The total cost of renovation not exceed the $19.7 million figure, unless the health planning agency makes allowances for inflation.

The new facility conform to architectural and health care plans already approved.

The new facility be limited to 260 beds, rather than the 321 approved for the I Street hospital.

The health planning agency, within 30 days, review proposed changes in the hospital's plans for its emergency room, intensive care unit and cardiac care unit facilities.

Control of the jospital remain with the present stockholders during the one-year period for which the certificate of need is being extended.

"We think [Doctors Hospital] is a real, vital, cog in the matrix of health care here in the center city," said medical staff president Jonas. Joans said 650 physicians are on the hospital's staff.

"Most of those doctors have offices in downtown Washington," he said, "and since the hospital plays a significant role in their health care, [closing the hospital] would have forced a significant number of them out to suburbia."

Jonas, and other supporters of the hospital, also point out that its average daily charge of $235 is $90 to $140 less than other major hospitals in downtown Washington.