The Treasury Department, which has been borrowing furiously in recent years to finance mammoth budget deficits, yesterday said that for the first time in three years it can pay off some of the $668.9 billion national debt.

Anthony M. Solomon, under secretary of the Treasury for Monetary Affairs, told reporters that because of the expected demise of the $50-a-person tax rebate, the agency suddenly finds itself with a "cash surplus."

As a result - instead of borrowing the many billions of dollars it planned to until recently - the agency will be able to reduce the national debt by about $2 billion over the next three months.

But the government's new-found affluence will be short-lived, Solomon said. He said he expects the Treasury will be forced to borrow between $12 billion and $15 billion in the three months which start July 1.

The last time the government was able to pay off any of its debt was in the second quarter of 1974, when it reduced the national debt by $6.8 billion. Since then the government has borrowed more than $180 billion as tax receipts sagged during the 1974-75 recession and spending programs climbed.

Even though the government will pay off some of the federal debt during the current quarter, for federal spending year 1977 as a whole (a fiscal year which runs from Oct. 1, 1976, until Sept. 30, 1977), the government is expected to run a deficit of $48.7 billion.

But that deficit is $19.3 billion smaller than the Office of management and Budget estimated it would be last February. Most of the downward revision, $12.2 billion to be precise, came about because President's Carter's sudden abandonment of the $50-a-person tax rebate assures it will not clear Congress.

Federal spending also is running below estimates and receipts are about $1 billion bigger than anticipated.

Solomon said that the Treasury already has paid off $500 million of the national debt and will pay off another $500 million or so in its regular quarterly refinancing of securities which mature on May 15.

On May 15, $4,283 billion of federal securities mature. The agency will issue two securities totaling $3.75 billion and will dip into its cash to pay off the remaining $533 million, Solomon told reporters.

The two securities the Treasury will sell next week include:

$2.75 billion of six-year, nine-month notes which will be auctioned Tuesday, May 3. The minimum denomination will be $1,000. The note carries a coupon which pays 7.25 per cent on the face value.

$1 billion of 29-year, nine-month bonds to be auctioned next Wednesday. The minimum denomination is $1,000. While the bonds mature Feb. 15,2007, the Treasury, at its option, can "call" them in after Feb. 15, 2002. The bond has a coupon which pays 7,625 per cent on the face value.

Solomon told reporters that because the Treasury is in good shape this quarter, it will try to lengthen the average maturity of the government's debt, by issuing relatively fewer short-term securities and relatively more notes and bonds with longer-term maturities.

At present, Solomon said, the average term of a federal security is about two-years, none-montsh.

The government pays off the federal debt by dipping into its own cash reserves to redeem maturing securities, rather than issuing new securities to pay off the maturing ones.

Solomon said that "for the quarter as a whole . . . there will be an increase in outstanding coupon issues, and . . . the reduction in marketable debt will be concentrated in bills. This means that there will be further and substantial reductions in the weeks immediately ahead and perhaps into June."

Solomon said that there also may be a need to float some very short-term cash management bills in June to help the Treasury during its cash shortage in the days before the June 15 corporate tax payment day.