District of Columbia court officials and a group of local lawyers, saying that budget cuts and a depressed economy have resulted in a critical lack of legal services for thousands of the city's poor, announced a major effort yesterday to enlist lawyers in representing people who cannot afford legal help.

The court officials and lawyers said the problem has reached near-crisis proportions, with federal budget cuts reducing staffs at the city's free legal service agencies while economic conditions are forcing increasing numbers of people into the courts with bankruptcies, evictions and other legal difficulties.

"It's no longer a matter of putting people on a waiting list," said Willie Cook, executive director of Neighborhood Legal Services, the city's largest legal assistance agency. "We just have to turn people away."

Jacob A. Stein, president of the D.C. Bar, announced that a letter from a consortium of the city's chief judges and other leaders in the legal community has been sent to about 24,000 Washington-area lawyers, urging them to volunteer to take cases.

Stein and the chief judges of D.C. Superior Court, the D.C. Court of Appeals, U.S. District Court and the U.S. Court of Appeals were joined by City Council Chairman David A. Clarke in announcing the enlistment drive at a Superior Court press conference.

D.C. Court of Appeals Chief Judge Theodore R. Newman Jr. told reporters that "it's too late to wonder whether adequate government funding should have been made available" to furnish lawyers for low-income clients.

Officials said they were unable to say precisely how many people are without legal assistance. Cook estimated that only 1 percent of nearly 200,000 city residents eligible for assistance under federal guidelines are receiving help.

Cook said he has been forced to fire 27 staff employes because federal funding for the agency has been cut by nearly one-third in the last two years. The number of cases the agency has been able to take has dropped from 10,000 in 1981 to 7,000 last year, he said.

On top of staffing problems, Cook said, the rolls of low-income people needing assistance have swelled in the economic recession, with hundreds facing evictions, foreclosures, bankruptcies and other financial difficulties.

D.C. Superior Court Chief Judge H. Carl Moultrie I said parents and children involved in neglect and abuse cases in the city's family court also are "facing a crisis" because there are not enough lawyers to represent them.

Moultrie said that at least 250 lawyers, each taking two cases a year, are needed to relieve the caseload in family court alone.