President Carter recommended yesterday that Congress approve a $61.8 million supplemental federal payment request for the District of Columbia, a key element of Mayor Marion Barry's attempt to balance the city budget.

There has already been discussion within Congress of not approving the full amount. Carter's nonbinding recommendation means that Barry's proposal will at least Capitol Hill intact.

There was no immediate statement from the White House yesterday indicating how hard the Carter administration would lobby for approval of the full amount, without which the city could face a budget deficit of up to $173.4 million for the current fiscal year.

The request for the extra federal payment, which was approved with minor changes last month by the City Council, is the largest single item in Barry's package of proposals to close the budget gap.

The request includes $21 million for pension payments to District workers, $14.5 million to cover pay raises already approved but for which no funds have yet been appropriated, more than $11 million for Department of Human Services programs and smaller amounts to cover increased fuel costs, space rental and other expenditures.

District officials said they were pleased by the White House action. But influential Capitol Hill sources reiterated their doubts that Congress would appropriate the full $61.8 million at a time when Congress is trying to curtail sharply federal spending.

"It would be a little silly for Congress to act on the request before knowing the fate of other portions of Barry's budget-balancing plan, particularly a $24 million package of new and increased taxes, one Capitol Hill source said yesterday.

The tax package must be approved by the City Council, which has been reluctant to act unless Barry proposes further personnel and program reductions.

Council Finance Committee chairman John A. Wilson (D-Ward 2) has scheduled hearings on the taxes to begin later this month, but has indicated he will not support the taxes unless Barry scales them down and makes corresponding increases in layoffs of city workers.

City Budget Director Gladys W. Mack said yesterday, however, that she was "very pleased" with the White House action. Without this step, we wouldn't even have had the chance to go to Congress," Mack said. "We will be able to present our full justifications for the request."