Roughly one-third of recent welfare applicants in Washington have had to wait longer than the legal limit of 45 days for their first payments or denial notices, according to the Neighborhood Legal Services Program, which is seeking a contempt citation against D.C. welfare officials in U.S. District Court.

City officials, who have been under federal court order since 1974 to speed up the processing of new welfare applications, said in court papers filed Tuesday that the current delays were caused by changed federal requirements, a new computer system, and "malfunctioning computer programs."

Robert I. Berlow, an attorney for Neighborhood Legal Services, said applicants for Aid to Families with Dependent Children (AFDC) payments have in some cases waited more than two months before learning whether they would receive checks from the city Department of Human Services.

"When you are talking about those individual persons' lives, that is severe," Berlow said. Last October and November, he said, about 800 families, or more than 40 percent of new applicants, did not receive checks or notices within 45 days, making it difficult for many to pay rent or buy necessities.

Berlow last week asked U.S. District Judge Aubrey E. Robinson to find Mayor Marion Barry and DHS officials in contempt of an order Robinson issued in 1974 compelling them to make timely payments. City officials were declared in contempt once, in 1978, for failing to comply. No hearing has yet been scheduled on the new motion.

The court action began in 1974 when the department had backlogs of as many as 2,000 applications per month and waiting time averaged more than 60 days. The court order required city officials to obey the 45-day limit imposed by city law, and to file monthly reports, which became known as Motley Reports--named for Annie Pearl Motley, the welfare recipient who initiated the action.

DHS documents filed in court this week indicate that at least 2,300 cases between last November and May took longer than the legal limit to decide.

Neighborhood Legal Services revived the eight-year-old court action last week because clients were again experiencing delays and because the city had failed since last August to file its Motley Reports, Berlow said.

DHS director James A. Buford reported to the court that new AFDC eligibility requirements passed by the Reagan administration forced DHS to use new forms and retrain its staff to determine eligibility for the program.

The corporation counsel's office told the court Tuesday that computer problems--now corrected--had made it impossible to send the Motley Reports.