The House of Representatives voted yesterday to prohibit the District government from using its own funds to pay for abortions for poor women, and cut $10.8 million from the annual federal payment to the city, in approving the fiscal 1987 D.C. budget.

The abortion amendment, passed after less than 10 minutes of discussion, is similar to restrictive language approved by the House last year. District officials, who contend the restriction encroaches on home rule, had to work hard last year to get it dropped.

The House prohibition goes beyond current standard language in appropriations bills that prevents federal funds from being used for abortions. The amendment would make the District the only jurisdiction in the country that could not use its own locally generated revenues to pay for abortions, which the city now does for poor women, according to opponents.

In approving the District's $2.6 billion operating budget and a $365.4 million capital budget yesterday, the House rejected an attempt to add $1 million to fight drug trafficking in the city by transferring the funds from the $2.4 million D.C. Arts and Humanities Commission budget.

Members also blocked a vote on an attempt to kill new D.C. legislation that prohibits insurers from denying coverage to persons who test positive for exposure to the AIDS virus.

The legislation, due to go into effect in early August, has become a target of the Moral Majority. A letter to members of Congress from a group called the Committee to Protect the Family, signed by the chairman of the D.C. Moral Majority, said that a vote against killing the bill "will be counted as a vote to legitimize the homosexual life style and to make the poor and average working families pay a bonus to AIDS virus carriers."

The District's appropriations bill was approved 296 to 117 and now goes to the Senate for consideration.

The amendment to cut the $425 million federal payment by $10.8 million, approved 230 to 176, was described by sponsor Rep. Bill Frenzel (R-Minn.) as a freeze in federal funding at fiscal 1986 levels, similar to amendments he has proposed on other appropriations bills.

City officials later expressed concern about the amendment, pointing out that it puts the city's budget out of balance.

"It puts a triple whammy to the District of Columbia," said Richard Siegel, the mayor's budget director, because it comes on top of cuts in federal funding caused by the Gramm-Rudman-Hollings deficit reduction law. "We have to be concerned."

The District's budget provoked more controversy yesterday on the House floor than it had in years. Members reacted strongly and sympathetically to House Minority Leader Robert H. Michel's tale of woe in seeking a variance and building permit from the D.C. government to build a two-car garage at his house.

Michel (R-Ill.) detailed a trek through the city bureaucracy over a period of months that included appearing before various local panels, waiting in line at one city office for 1 1/2 hours and still not having the building permit in hand.

Dwight Cropp, the mayor's director of intergovernmental relations, said later that Michel had been informed that the building permit was ready two days ago.

The most debate revolved around the amendment by Rep. Robert S. Walker (R-Pa.), defeated 229 to 183, to transfer $1 million of the arts funding to drug enforcement, with opponents charging that it was a sham.

Rep. Julian C. Dixon (D-Calif.), chairman of the House Appropriations subcommittee on the District, said during a testy exchange with Walker that the police department already requested and received a $10 million increase as part of its $157.8 million budget this year to help fight drugs.

"It's very cosmetic . . . a piddling amount," Dixon said of Walker's proposal.