Cuts in the federal payment to the District of Columbia ordained by the Gramm-Rudman-Hollings law will be smaller than those calculated last week by the Office of Management and Budget and the Conngressional Budget Office, according to a report issued yesterday by the U.S. comptroller general.

The result likely will be $6.7 million more for the city this fiscal year than had been expected a week ago. OMB and CBO last week reported that the federal payment of $547 million should be cut $23.5 million, but the comptroller general revised the figure to $16.8 million, saying the budget agencies had erred.

At the same time, the comptroller general, who heads the General Accounting Office, settled a dispute over federal interest payments on nearly $1 billion in bonds issued to help build the Metro subway system. The GAO chief ruled that no cut in these payments is required under the deficit reduction law. Officials had warned that a cut might lead to a default on the bonds.

Alphonse G. Hill, D.C. deputy mayor for finance, who had protested the cuts announced last week, said he remained unhappy with the new reductions, in part because GAO did not appear to have accepted his argument that the federal payment for water and sewer services should be exempted from the Gramm-Rudman-Hollings reductions.

"This logic still doesn't make sense to me," Hill said of the comptroller general's report. The report was submitted yesterday to President Reagan, who must order the cuts by March 1 unless he and the Congress can agree on an alternative, which is considered unlikely.

The GAO calculations, reducing the cuts from $23.5 million to $16.8 million, were obtained by treating the overall federal payment as six separate accounts, rather than as a single account as the OMB and CBO studies had done.

The result was a determination that because the largest account had been largely spent, a limited amount of funds remained to be cut. "We take what's left," said Harry Havens, assistant comptroller general.

The comptroller general also ordered a change in funding cuts for St. Elizabeths Hospital, determining that OMB and CBO had listed a $25 million payment for the hospital in two accounts and effectively cut the payment twice.

"Our objective here was to make sure that the $25 million did not get hit a second time," Havens said.

The cuts represent the first round of reductions under the deficit reduction legislation. Overall, the budget offices ordered an $11.7 billion reduction in federal outlays, trimming 4.9 percent from the military and 4.3 percent from domestic agencies.

The dispute over the Metro bonds, resolved by GAO, stemmed from a conflict between CBO and OMB. The two agencies agreed that the federal interest payments should be spared from cuts, but they differed about whether cuts were mandated by the deficit reduction law.

At issue was a plan to cut $2.2 million from the federal government's annual $51.7 million payments on the bonds, which are federally guaranteed. If the government defaulted on the payments, officials said, the guarantee would leave the government "liable for the full payment" on the $997 million issue.

In ruling that the bond payments are exempt from cuts, the comptroller general largely agreed with CBO's arguments. The GAO head said the payments are "not subject" to cuts because the funds were "obligated" under a congressional appropriation.

The Metro transit authority still faces other major cuts under the deficit reduction measure, standing to lose $9.8 million this year in subway construction funds along with several million dollars in other federal aid. Federal officials have proposed cutting off all construction funds next year.