A key House subcommittee yesterday approved a record high federal payment for the District of Columbia next year that includes funds to save the jobs of 404 police officers and 100 teachers, and to provide a modest pay increase for city employers.

In granting Mayor Marion Barry most of what he asked for in a $1.5 billion operating budget that the mayor has described as austere, the House D.C. Appropriations subcommitte agreed to a federal payment of $296.6 million. If ultimately approved by both houses of Congress, that would be $20 million more than the payment for this fiscal year.

The subcommittee refused to go along with Barry's plan to cut the police force by 404 officers as part of his citywide economy drive.

At the insistence of Reps. William H. Natcher (D-Ky.), the subcommittee's former chairman, and Carl D. Pursell (R-Mich.), its ranking minority member, the panel provided $4.6 million that the mayor did not request. It said these funds should be used to prevent a reduction of the police force by 204 through layoffs and 200 more through attrition.

The subcommittee, on the recommendation of its chairman, Rep. Julian C. Dixon (D-Calif.), added an unrequested $1 million to the school budget to provide for keeping 100 teachers on the payroll who otherwise would face layoffs.

The subcommittee also approved Barry's request for $36.5 million to grant more than 35,000 city employes a cost-of-living pay increase of 4.8 percent. That would be far short of the 7.8 to 13.5 percent raise that federal workers may receive at the start of the fiscal year Oct. 1 as a result of expected presidential action.

Barry notified the City Council last month that he was not recommending any pay increase for municipal employes for the present, citing the city's tight finances and uncertainty stemming from the lack of congressional action on the 1981 budget.

The mayor, a spectator at yesterday's subcommittee meeting, said afterward that he would recommend the 4.8 percent pay rise if the funds to provide it remain intact when Congress approves the final version of the budget.

In a related development, the City Council enacted legislation yesterday to make clear that the city -- breaking with a tradition dating from the years when it was treated like a federal agency -- can now depart from the pay scales and pay raises granted federal workers.

Officials of unions representing city employes warned at a council hearing Monday that they consider such a step to be illegal, and may challenge it in court.

Yesterday's subcommittee action is the first of at least nine steps the city budget must take in the labyrinthine path through Congress. Ordinarily, however, the House subcommittee action sets the basic pattern for final action.

Yesterday's subcommittee meeting was held in a business-as-usual atmosphere, with none of its members even mentioning the city's well-publicized budget crisis or the mayor's warning that the city would run out of money if it is refused authority by Congress to borrow $215 million.

The budget as approved yesterday is balanced under a new city accounting method, Barry noted, and will not add to the city's accumulated deficit, which will reach as estimated $409 million by Sept. 30.

The budget will reduce the number of authorized city jobs from 37,886 in the current fiscal year to 35,268 next year. Not all those positions are currently filled.

It also calls for an array of program reductions, including the withdrawal of an earlier proposal to grant a 5 percent cost-of-living increase in payments to welfare recipients. That action will save $3 million.

At the insistence of Rep. Gunn McKay (D-Utah), the subcommittee voted to keep a proviso in the budget that bans the District from spending any federal Medicaid funds to pay for abortions for the city's poor women.

That proviso was added last year by a Senate-House conference committee, and Subcommittee Chairman Dixon yesterday supported the mayor's request to have it removed. Dixon acquiesced to McKay to avoid what he called a divisive subcommittee vote.

Nellie Gray, president of D.C. Right to Life, said her group would continue lobbying to get Congress to bar the District from spending its own funds for abortions.

The only other controversy at yesterday's meeting was sparked by Rep. Louis Stokes (D-Ohio), who said the subcommittee's decision to add the police funds was contrary to the principle of District home rule.

Barry, voicing general satisfaction with the budget measure and especially the higher federal payment, said he was "very disturbed that the police and teachers took it upon themselves to violate the principles of home rule" by lobbying Congress for more money than the mayor and council had requested.

Larry Melton, vice president of Loxl 442 of the International Brotherhood of Police Officers, said his members were "acting responsibly for the safety of the people."