The federal government yesterday loaned New York City $255 million that will enable it to pay bills totaling more than $125 million early next week.

Treasury Secretary W. Michael Blumenthal said the federal government had to wait to approve the $255 million needed to keep New York City going until the city came up with an acceptable plan to pay off holders of $983 million of past-due city notes. The city announced such a plan Wednesday.

The latest loan - part of a federal program that allows the city to borrow up to $2.3 billion a year to cover its seasonal cash lows - puts New York City $2.1 billion in debt to the U.S. Treasury.

New York City will have to pay that amount by June 30, the end of its fiscal year, with the heavy flow of tax receipts it gets in June. The city will then be able to come back to the federal government for loans of up to $2.3 billion more to cover its seasonal cash shortages in the spending year that starts July 1.

Before the Treasury can disburse any money to New York City, it must decide that the city can repay the money by the end of the fiscal year.

As part of its plan to get spending under control and eliminate an accumulated budget deficit of $1 billion, New York City had decided not to repay notes that had matured for three years. Last November, however, the state's highest court, the New York Court of Appeals, declared the three-year moratorium unconstitutional, and New York City and its state-appointed financial overseers have been trying to devise a plan to pay off the $983 million in past-due notes held by individuals.

Blumenthal told reporters yesterday that he considers the new plan "adequate to ensure the city's solvency during this 16-week period" until the end of June when the city must repay the $2.1 billion it owes the Treasury.

But Blumenthal warned, as he has before, that further seasonal loans will depend on New York City's ability to keep its financial house in order and said that if the city is to keep its budget balanced over the long run, permanent reforms will be required.

The plan devised by city officials to pay off the $983 million in past-due notes may not work, city officials concede. It relies heavily upon the willingness of owners of about $250 million of the notes to swap them for new municipal securities.

Felix Rohatyn, a member of the Emergency Financial Control Board that now oversees the city's financing, gave the package a "70-30 chance of squeaking through without any problems." Rohatyn is also chairman of the Municipal Assistance Corp., a state corporation that borrows money on behalf of New York City.

Besides swapping $250 million of new securities for past-due ones, the city plans to pay off the rest of the $983 million with money realized through selling $410 million in mortgages it owns on some middle-income housing projects, postponing repayments to union pension funds and a variety of other smaller sources.

The $255 million federal loan will have nothing to do with repaying the past-due notes but rather will be used to keep the city running.

Following the Treasury announcement of the approval, New York City Mayor Abraham D. Beame said the loan "lifts a major financial burden from the shoulders of the city." Beame said the city must "continue to maintain its austerity program."

New York City needed the federal loan program because its accumulated debt of more than $1 billion in 1975 cut the city off from borrowing in the normal money markets to meet its seasonal cash needs. President Carter has said that when the current loan program expires on June 30, 1978, the administration will consider extending it to ease the shock.

New York City's banks had devised a plan that would have sent the city into the money markets to borrow some funds to pay off the $983 million of past-due notes. Beame angrily rejected the plan because it would have created a new board to oversee the city's finances, which would have removed almost all financing authority from the city officials.

The banks did not participate in the plan devised earlier this week by the city.

New York has whittled that accumulated deficit down from more than $1 billion to around $450 million through program cutbacks and it hopes to have fully erased it by June 30, 1978.

City officials estimate that New York City will have to borrow $3 billion a year to cover seasonal cash needs in the spending year that begins July 1, 1978, and $1 billion for longer-term capital needs.

Blumenthal told reporters yesterday that the administration should have a plan to Congress by mid-year that will propose a mechanism - such as a special bank or loan guarantee facility - to help hard-pressed cities, not just New York, get the money they need, especially for capital projects like building.

Blumenthal said any proposal the administration sends to Congress is "likely to have strings attached for cities taking advantage of it," such as federal supervision of their finances.