With only 19 of its 435 members on the floor, the House needed just 10 minutes yesterday to give its final approval to a District of Columbia budget that required Mayor Marion Barry to hire about 200 more police officers that he believes are not needed.

The Senate is scheduled to act today, sending the $1.5 billion operating budget and $221 million public works program to President Carter for his expected signature.

In its dollar amount, the congressionally approved operating budget for the fiscal year that began Oct. 1 differs little from the city's original request. But in enacting it, Congress imposed its will on the city's nearly six-year-old home rule government by telling it to beef up the police force, which has dwindled from a peak of 5,100 officers in 1972 to 3,660 now.

Barry had proposed to let the force drop to 3,359 by next Sept. 30 as part of the city's economy drive despite an increase in reported crime that has sent the city's crime rate to its highest level in nearly a decade.

In its official report to both chambers of Congress and adopted yesterday by the House, a joint conference committee that reconciled the differing House and Senate versions of the budget ordered that "no further reductions [in the police force] be made . . . below the current level."

The conferees, the report continued, "further direct District officials to move aggressively toward a hiring and training program that will bring the employment level . . . above the level of 3,800 filled sworn police officer positions immediately."

The provision was demanded by Rep. William H. Natcher (D-Ky.), the long-time advocate of a large police force to protect citizens and tourists, with support from the House D.C. Appropriations subcommittee's new chairman, Rep. Julian C. Dixon (D-Calif.).

Barry was out of the city yesterday and his press office had no comment on the congressional action. Barry had said earlier that he would reluctantly obey the congressional directive.

The police department currently is screening applicants and hopes to start training a class of 25 new officers later this month, according to Joseph Gentile of the department's public relations office. He would not speculate on how soon the department could recruit enough applicants to meet the congressional mandate.

Personnel officials have said recruiting has been slowed by a new law that requires newly hired employes to live in the District.

While the congressional report mentions a goal exceeding 3,800 officers, an aide to the House D.C. Appropriations unit said that number is a minimum and its members hope the city eventually will reach the 3,880 officers whose salaries are provided in the budget.

Yesterday's House action, approval of the conference report, was taken by unanimous consent of the 19 members on the floor without any vote. It provides the city with a record federal payment chiefly in lieu of taxes of $295.4 million, almost precisely what the city requested.

While the operating budget remained substantially intact in its review by Congress, the city's public works construction program was pruned from the requested $256 million to $221 million. Several urban renewal, transportation, health, police and fire department projects were eliminated.

Rep. Carl Pursell (R-Mich.), ranking minority member of the Appropriations subcommittee, noted that the operating budget is only 6.8 percent larger than last year's budget. In a bit of praise for city officials, rare on the House floor, he declared, "I can't accuse the D.C. leaders of high spending when we are under the [national] inflation rate."