A congressional conference committee yesterday recommended a federal payment to the District of Columbia of $240 million in the 1981 fiscal year which is $60 million less than the city had hoped for.

If accepted by both houses of Congress, the recommendation by the joint House-Senate committee would throw the District's proposed $1.5 billion operating budget out of balance by the $60 million and force cuts in spending greater than those already proposed by Mayor Marion Barry and the City Council. President Carter has endorsed the city's request for a $300 million payment.

The $240 million proposed payment is about the same as Congress has provided to the District so far this fiscal year. The House soon will consider a $28.8 million supplemental payment.

Barry learned of the proposed cut while being interviewed on television. He looked stunned, and when pressed for a reaction, said, "Don't blame me for the inaction of the Congress . . . you ought to ask the Congress."

The level of the federal payment is included in a resolution setting the proposed level of the national budget for 1981 at $613 billion. The District's proposed payment is buried in a category that calls for $6 billion in aid to the nation's states and cities.

Under congressional procedures, only broad categories ultimately will be binding on the appropriations committees that actually grant the funds. Individual items such as the District payment can be adjusted upward or downward as long as the category expenditures totals remain the same.

The conferees actually recommended a total of $301 million for the District, but that figure would include a $52 million federal pension subsidy and an $8 million sewer and water service payment in addition to the outlay to help finance the city budget.

The federal payment is made annually to compensate the city for taxes it cannot collect on federal and other tax-exempt properties and for services the city government provides as the nation's capital.