Congressional negotiators agreed early today to give up to $38.3 million as an additional federal payment to the District of Columbia, far short of the funds sought by Mayor Marion Barry to finance city operations for the rest of the fiscal year.

Barry had sought $61.8 million as part of his effort to avert a budget deficit. The House agreed recently to provide only $28.8 million, a figure late raised by the Senate to $45.3 million.

But the House-Senate conference committee this morning trimed the figure back to a maximum of $38.3 million after a dispute erupted over Barry's agreement last week to cancel $20 million in municipal construction projects in order to get an identical sum shifted to pay city operating costs.

Of the $38.3 million, $6.8 million is conditioned upon the city providing a revised list of canceled construction projects.

This morning's agreement is subject to final vote in both the House and Senate, but no change is expected.

Senator Patrick J. Leahy (D-Vt.), chairman of the Senate D.C. Appropriations Subcommittee, said Barry's list that was said to contain $20 million in cancelled projects actually boiled down to only $7 million in truly canceled projects. So Leahy moved to grant the city only that amount and not the full $20 million in extra operating funds.

A Leahy aide said many of the projects on the mayor's list were already under way or so far committed that they could not be considered for cancellation. A list of the disputed projects was not immediately available last night.

Senator Charles McC. Mathias Jr. (R-Md.) argued that city officials should be trusted to keep their end of the deal to cut their construction programs by $20 million.

"This city will blow up [financially] on us sometime before the next couple of months are out," Mathis said, "And we ought to face it here tonight . . . having the city default on its bils . . . that's what you're facing."

Senator Thomas F. Eagleton (D-Mo.) said the city has a "very severe cashflow problem, no question about that -- severe."

After reaching an impasse, Leahy, Mathias and Rep. Julian C. Dixon (D-Calif.), chairman of the House D.C. Appropriations subcommittee met privately and worked out a compromise. The city must now provide a list of $6.8 million in additional projects to be cut, and get the list approved by both Leahy's and Dixon's subcommittee before it gets the $6.8 million for operating expenses.

District budget director Gladys W. Mack was informed by a Senate aide immediately after the compromise agreement. She said she could not say immediately what effect the reduced supplemental payment would have on the city's efforts to avoid a budget deficit that may run as high as $172 million before the fiscal year ends in October.

Barry had sought the $61.8 million which he hoped to add to a package of new taxes that the City Council enacted yesterday to help balance the city budget. The mayor also has announced a freeze on city hiring, layoffs and other economy moves designed to save $50 million in operating expenses.

The agreement came about 12:30 a.m. as the conference committee plowed through a supplemental appropriations bill that will provide upwards of $15 billion, chiefly to federal agencies to keep them running through the rest of the fiscal year, which ends Sept. 30.

The District supplemental bill is a tiny fraction of the overall bill.

All of the money to be appropriated to the District is going to pay bills already incurred, and increased costs of such items as energy and pensions.

The $38.3 million would bring the city's federal payment to a total of $274 million for the current fiscal year.

The city also has pending on Capitol Hill its proposed budget for the 1981 fiscal year.

Dixon's subcommittee has scheduled a meeting for today to act on that budget, which totals $1.5 billion and contemplates a federal payment of $300 million as the U.S. share of city operations.