The House gave solid approval yesterday to a set of final budget ceilings for fiscal 1979, after narrowly rejecting a GOP-sponsored proposal that would have cut spending by another $10.4 billion.

The Senate is scheduled to take up a similar resolution next week. When the two versions are reconciled by a conference committee and endorsed by both houses, the ceilings will be binding.

The action marked the next to the last step in a process, enacted four years ago, that has enabled Congress to substitute its own formal tax and spending plan for the budget the president sends the lawmakers in January.

The spending levels approved by the House yesterday were $9.8 billion below the $500.2 billion President Carter sought in January, and $8.3 billion below the tentative spending targets Congress set last spring.

Yesterday's measure called for a deficit of $43.7 billion - $16.9 billion below what Carter proposed in January and $7.2 billion lower than Congress estimated in its tentative resolution.

However, most of the reductions refelct re-estimates of program costs and interest charges, rather than sweeping changes in Carter's budget. The congressional figures also provide for a smaller tax cut than Carter's did.

Approval came after the House agreed on a vote of 271 to 134, to a proposal by Rep. James A. Mattox (D-Tex.) to trim $335 million from the public jobs program and $338 million in fiscal aid to states and cities.

However, the vote was regarded as little more than a token gesture. Virtually all sides are seeking to trim back the jobs and fiscal aid programs as the economy heads toward full employment.

Defeat of the Republican proposal to cut $10.4 billion came on a close 206-to-201 ote, with 61 Democrats supporting the GOP plan. The margin had little real significance, however. The plan was regarded as a "free vote" for Democrats to endorse spending cuts.

House members also rejected, 241 to 155, a proposal by Rep. Joseph L. Fisher (D-Va.) that would have cut spending by a flat 1 percent in all government programs and departments, regardless of merit.

The ceilings approved yesterday would hold spending levels to $490.487 billion for the fiscal year beginning Oct. 1, with expected tax revenues estimated at $446.8 billion and a deficit of $43.687 billion.

By comparison, the tentative targets Congress approved last spring called for spending of $498.8 billion, with revenues of $447.9 billion and a deficit of $50.9 billion.

Overall budget authority in yesterday's resolution was $561.506 billion, compared with $568.850 in the targets set this past spring. The figure includes spending for this year and obligations for coming years.

When the final version of the budget resolution is approved by both houses, it serves as a binding ceiling for all appropriations and tax bills. Any proposal that violates the ceilings may be ruled out of order.