Representatives of the District of Columbia courts said yesterday their backlog of pending cases is at an all-time high, and they asked Congress to increase their fiscal 1984 budgets from the levels recommended by the D.C. city government.

"If we had no filings for one year, we would not be able to eliminate the backlog" of cases in the D.C. Court of Appeals, said Chief Judge Theodore R. Newman Jr. at Senate subcommittee hearings yesterday.

The court actually anticipates a 20- to 25-percent increase in the number of filings in 1983, he said. Newman said that last year his court disposed of more cases than ever before, but still lost ground on the backlog because of the volume of new cases.

The average time for resolving a case before the appeals court in 1982 was 544 days, or about 1 1/2 years, an increase of 36 days from 1981, he said. This average is substantially worse than in comparable courts in other jurisdictions, said Larry P. Polansky, executive officer of the D.C. courts.

Newman and Polansky made their remarks at the second day of hearings in the Senate Appropriations subcommittee on the District of Columbia on the city's fiscal 1984 budget. The subcommittee also heard from the U.S. attorney for the District of Columbia, the D.C. corporation counsel, the police chief and the director of the corrections department, all of whom said they could live within their fiscal 1984 budgets as approved by the city.

The D.C. City Council and Mayor Marion Barry have approved a budget for the next fiscal year, which begins Oct. 1, but Congress still must pass it and can amend it first.

D.C. Superior Court Chief Judge H. Carl Moultrie I told the subcommittee that the city is requesting $3 million less in fiscal 1984 than "the minimum necessary to continue to effectively operate" his court. He also repeated a previous request for seven judges to be added to the 44 at the court now.

At the end of 1982, there was a backlog of 38,000 cases before Superior Court, Moultrie testified. As of last fall, it was taking 185 days to dispose of felony cases, one year for domestic cases, and more than two years for civil cases, according to court figures presented to the subcommittee.

"The court's burden, already overwhelming, has been exacerbated by pending caseloads which are at an all-time high," as well as crime crackdowns and new laws that the court has to administer, he said.

Subcommittee Chairman Arlen Specter (R-Pa.), a former district attorney in Philadelphia, told the judges he is "prepared to take a close look at your situation." He noted that federal courts have said they need more resources to deal with all the cases before them and that "similar consideration is in order for your courts." Congress will continue to examine the District budget over what is now an indefinite time period.

Police Chief Maurice Turner said crime has dropped 12 percent so far this year, which he attributed to the new emphasis on identifying and prosecuting "career criminals."