The House of Representatives yesterday narrowly rejected a strong effort to ban publicly financed abortions in the District of Columbia. It also voted, in approving the city's budget, to cut $6 million from the expected federal financing for city operations during the coming fiscal year.

Its 192-to-182 vote on abortions after nearly two hours of heated debate cleared the way for early Senate action and final enactment of the city's 1981 budget. The adoption of budgets for the past three years had been delayed by disputes over the emotion-charged issue.

The House's 218-to-144 vote to cut $6 million from the federal payment of $296.6 million recommended earlier by the Appropriations Committee apparently will throw the city's already tight budget out of balance. That would require further cuts in city programs of a rescue operation by the Senate.

The federal payment, made annually, is designed to compensate the city for taxes it cannot collect of U.S. and foreign embassy property and for unusual costs resulting from the city's status as the nation's capital. More than $1.2 billion of the $1.52 billion operating budget is financed from local taxes.

The operating budget, adopted by a final roll-call vote of 215 to 158, will permit the city to continue spending its own locally raised tax money to provide abortions for poor women under the Medicaid program. It continues a near-total ban, imposed last year, on spending U.S. funds for that purpose. a

Rep. Robert K. Dornan (D-Calif.) proposed an amendment that would have imposed an absolute ban on all publicly financed abortions.

"Abortion is the great moral issue of today as was chattel slavery in the last century," Dornan said.

"Mayor (Marion) Barry was surprised to learn a few weeks ago that the population of D.C. is declining," Dornan said in sarcastic tones, blaming the large number of abortions for a drop this year estimated at 100,000 from the 1970 census figure of 756,000.

In the past year, the city spent $1.3 million for 5,700 Medicaid abortions, according to official figures. Each year since 1975, Dornan said, the number of abortions in the city has exceeded total live births.

Opposition to Dornan's proposal was spearheaded by Rep. Julian C. Dixon (D-Calif.), a Washington native serving his first year as chairman of the D.C. Appropriations subcommittee.

Perhaps the most telling opposition came from Rep. Tim Lee Carter (R-Ky.) and Rep. Shirley Chisholm (D-N.Y.). Carter, a physician said Dornan's proposal would prevent abortions needed to save the lives of mothers. dChisholm, her voice rising with emotion, told of visiting hospital wards and seeing women recovering from efforts to self-induce abortions.

Del. Walter E. Fauntroy (D-D.C.), a Baptist minister who voiced personal reservations about abortions, opposed the amendment and contended that its adoption would erode the congressional grant of limited home rule to the District of Columbia in 1975.

Rep. Stewart B. McKinney (R-Conn.), ranking minority member of the House District Committee, elaborated on that theme, calling the continued congressional control of the nation's capital "a blotch, a smear and an obscenity on the American political process . . . implausible and decadent."

Rep. Henry Hyde (R-Ill.), who has given his name to previous House amendments restricting abortion, disputed that view. He said abortion opponents often have adopted views that curtail state and local rights in such areas as school busing for racial balance.

The stage was set for yesterday's abortion vote by a recent Supreme Court ruling that Congress has the power to ban the use of federal funds to pay for abortions. The same ruling upheld the right of the states to pay for Medicaid abortions from their own funds.

Nine states and the District of Columbia use their own money for that purpose, but D.C. is the only jurisdiction whose budget is reviewed by Congress.

Leaders of proabortion groups applauded the House action. "I think it represents . . . an affirmation that the people in D.C. should have home rule on this issue," said Leslie Harris, executive director of the D.C. American Civil Liberties Union chapter. Pam Barnett, legislative coordinator for the Religious Coalition for Abortion Rights, claimed credit for members who lobbied against Dornan's proposal.

The cut of $6 million from the expected federal payment came on a motion by Rep. Clarence Miller (R-Ohio), who has sought with mixed results to cut 2 percent from each of the appropriation bills -- mainly for federal departments -- as they are considered by the House.

Miller had won similar efforts earlier this year to cut the budgets of the U.S. Department of Housing and Urban Development and of Congress itself.

Supporting him, Rep. James E. Collins (R-Texas) said that too many Washingtonians are on welfare and that their publicly financed idleness gives them time to commit crimes. These people "could work on ditches, wash dishes . . . all kinds of basic jobs," Collins said. No one replied to him.

Among Washington area legislators, only Rep. Marjorie Holt (R-Md.) voted for both the Dornan and Miller amendments. All others opposed it.

As approved by the House, the bill sets a ceiling of 35,268 D.C. employes, a drop of 2,618 below the current ceiling; requires the D.C. government to maintain a police force with at least 3,880 uniformed officers, and provides $35 million to grant a 5 percent pay increase to city employes. This is below the 9.1 percent recently approved for most federal employes.