The House is expected to be confronted again next week with the problem of authorizing billions of dollars for the nation's intelligence agencies in almost complete ignorance.

Rep. Romano Mazzoli [D-Ky.], a member of the House Intelligence Committee, intends to offer an amendment that would lift the secrecy just enough to force publication of the total spending in the authorization bill.

The Carter administration has no objection to the idea. Neither does the Central Intelligence Agency. But the House has turned out to be more protective.

Mazzoli says he has little hope of a majority, but wants to "keep people thinking about why they make the decisions they do." He offered his amendment in committee sessions this year and last, and was voted down both times.

"Even at times when the [Central Intelligence] Agency had a much worse reputation than it does today, these kinds of attempts have failed," said a House Intelligence Committee staff member.

The House measure would authorize undisclosed sums for the conduct of "intelligence-related activities" by the CIA, Department of Defense, Defense Intelligence Agency, National Security Agency, Army, Navy and Air Force, and the Departments of State, Treasury and Energy, FBI and Drug Enforcement Administration.

Total spending for these activities, according to a suppressed report of the House Intelligence Committee that leaked in 1976, was estimated to exceed $10 billion. That figure apparently included both direct and indirect costs.

Committee Chairman Edward P. Boland [D-Mass.] said his committee voted against disclosing the sum this year and last year because, "the majority feels it would lead to more questions being asked."

The public, Boland said, "would want to know why, for instance, if the budget has a particular bulge in it one year or not the next . . . . We don't want to deal with these questions."

"I don't think the American public is particularly interested in that figure anyway," he added.

The committee keeps a "Classified Annex" in its office that House members can read to learn details of the authorization measure, but few have bothered since the system was established last year. Critics say the secret document is so crammed with code words and acronyms that it makes little sense to outsiders.

In testimony before the committee last year, CIA Director Stansfield Turner said: "The administration does not object to $ Congress releasing to the public a single overall budget figure of the U.S. intelligence community." But Turner said he opposed breaking down the figure into its components.

The FBI discloses the amount it spends each year for domestic counterterrorist projects -- authorized this year at more than $13 million -- but does not reveal how much it spends to combat foreign espionage in the United States.

"In that area, you're dealing with adversaries with sophisticated intelligence apparatus, and they could scan a budget and determine what resources are being used," explained FBI spokesman Homer Boynton. "We want to give them as little information as we can."

Treasury Department spokesman Jack Plum said the department's intelligence budget is used to monitor financial exchanges and the actions of central banks in foreign countries.

"I frankly don't know why there's any reason to keep that quiet," Plum said.

The Senate Intelligence Committee, headed by Sen. Frank Church [DIdaho] found in 1976 that U.S. intelligence efforts then totaled 3 percent of federal spending, "but 8 percent of controllable federal spending." About 75 percent of federal spending for fiscal 1976 -- such as payments from the Social Security trust fund -- are described by the administration as "uncontrollable."

The committee at that time reported a lack of control over intelligence spending by either the White House Office of Management and Budget or by Congress.

The House Committee on Intelligence reported this year that the total authorization for 1980 intelligence spending is substantially larger than the amount authorized last year, but less than the administration requested.

The U.S. Constitution provides that "a regular statement of account of the receipts and expenditures of all public money shall be published from time to time," but the debate over whether this applies to intelligence spending has yet to be resolved. CAPTION: Picture, Gresso, left of microphones, and Carey, right, talk to reporters at National Airport on way to Camp David. AP