Mayor Mrion Barry Warned the administrators of the city's 12 major private hospitals yesterday that the maintenance of their tax-exempt status depends upon their providing a reasonable amount of free medical care to the city's poor.

Barry also reminded the administrators of the city's power to grant and deny licenses and to give permission to expand. The mayor met with the administrators for more than 1 1/2 hours to discuss the question of private hospitals transferring poor patients to D.C. g/eneral, the city's only public general hospital.

According to Charles OTBrien, administrator of Georgetown University Hospital and president of the D.C. Hospital Association, the private hospitals provided $14 million in "free or below-cost care last year." That care accounts for $13.30 on every paying patient's bill, O'Brein said.

Additionally, O'Brien said, the hospitals incurred $10 million in bad debts, adding another $10 per day to the average bill.

Barry said he wanted to know the total amount the hospitals billed patients during the year to decide if $14 million is a reasonable amount of free care.

Barry called the meeting yesterday after the publication of reports in The Washington Post that 713 patients were transferred from private hospitals to D.C. General in a 13-month period, and that about 463, or 90 percent, or those patients had no medical insurance.