District of Columbia officials, faced with a potential contempt of court citation in a suit brought by Lorton Reformatory inmates, yesterday agreed to reduce overcrowding and improve conditions at Lorton's central facility or pay substantial daily fines until those conditions are improved.

At a hearing yesterday before U.S. District Court Judge June L. Green, attorneys for the city and the inmates said they had essentially reached agreement in principle and requested more time to work out the details.

Green, who has presided over a long-running lawsuit on behalf of Lorton inmates since it was filed in federal court in 1980, indicated approval of the broad aspects of the agreement in a telephone conference with both sides a few hours after the hearing. She is expected to formally endorse the agreement on Thursday.

Peter J. Nickles, an attorney representing the inmates, said the city agreed to reduce within 90 days the number of inmates held at the central or medium-security facility to its rated capacity of about 1,100. That would be a reduction of about 300 inmates from its current population, Nickles said.

He said if the city does not reduce the inmate population at Lorton's central facility to 1,100 within 90 days, it will pay $1,000 a day in penalties for the first 30 days it is not in compliance, $5,000 a day for the next 60 days and $10,000 for every day after that if the number of inmates is not below or near the capacity.

The agreement applies only to Lorton's central facility and not to the maximum-security or other facilities in the Lorton complex.

Corrections officials anticipate they will be able to meet the agreed-upon deadlines concerning overcrowding through increased use of halfway houses, increased use of job programs to speed parole for Lorton inmates, continued expansion of Lorton facilities and normal attrition of prisoners at Lorton, according to one knowledgeable city official.

The overall Lorton population soared last month after corrections officials, faced with disturbances at the D.C. jail and another lawsuit involving overcrowding there, shuttled some 450 jail inmates to Lorton.

D.C. Corrections Director James F. Palmer, in a statement filed with Green earlier this month, has said that no new inmates will be sent to the medium-security facility until the number of inmates there is reduced to approximately 1,100, that official said.

Palmer's statement assumes that the population at the D.C. Jail will not exceed 2,100 inmates. City officials yesterday said the jail population, which had been as high as 2,400, was down last week to below 1,900.

City officials and Nickles yesterday reached agreement on a timetable for completing some 20 other improvements at the facility this year. Those include improving security, spending more money on training facilities, expanding and improving the staff, providing food services to the inmates and constructing new cells.

The city has agreed in principle to pay $250 a day in fines for every day that it fails to meet the deadlines on each item. In addition, the city, under the agreement worked out yesterday, has agreed that if it is not in substantial compliance with the terms of the agreement by January 1984, a special court-appointed master would take over administration of the Lorton central facility to make sure the improvements were made.

Nickles said yesterday that the agreement was "a last effort to give the city an opportunity to provide the inmates at Central with minimum facilities for living."