Interest rates continued to fall yesterday, as banks across the country lowered their prime lending rates from 10.5 to 10 percent, the lowest in more than six years. The Veterans Administration also dropped the maximum interest rate on its federally backed mortgages from 12.5 to 12 percent.

The falling interest rates reflected the actions of the Federal Reserve Board, which announced Friday that it was lowering the discount rate -- the interest at which the Fed lends money to banks -- in response to worries about the economy's health.

Yesterday was the first day for the stock market to react to the Fed's decision, and react it did. The Dow index rose about 19 1/2 points, closing near the 1305 level. The previous record close of 1,299.36 was set on March 1.

The stock market performance and the interest-rate decline were a few bits of good economic news in the midst of signs that the government today could revise downward its estimate of real growth in the first quarter from 1.3 percent to a negative figure.

In still another piece of good economic news, the Commerce Department reported that Americans' after-tax income rose a record 2.9 percent in April. Personal income before taxes rose 0.6 percent, following a 0.5 percent rise in March.

The Treasury Department announced yesterday that the average discount yield on three-month Treasury bills at yesterday's auction was 7.28 percent, compared with 7.69 percent last week. On six-month bills, it was 7.43 percent, down from 7.90 percent a week before.

The average yield on three-month bills was the lowest since June 23, 1980, when the average was 7.077 percent. The six-month average yield also was the lowest since June 23, 1980, when the average was 7.108 percent.

Notwithstanding what appeared to be some good news on the economic front, the National Association of Business Economists yesterday said that the economy may fall into a mild recession next year.

Although the personal-income report on its face appeared to dispel suggestions that economic sluggishness may not continue into the second quarter, economists said that extraordinary events and not underlying strength contributed to the 0.6 percent rise in personal income. Those factors were a retroactive wage payment of $3.1 billion to Postal Service employes and special payments to farmers, Commerce Department Chief Economist Robert Ortner said.

Without those factors, personal income would have risen only 0.4 percent, Ortner said. Economists look at personal income to gauge future strength in consumer spending and subsequent growth in the economy.

In addition, the 2.9 percent jump in after-tax income was largely because of the receipt of federal income tax refunds in April that usually are received in February and May.

"The increase in personal income is 0.6 percent, but the underlying strength is really less than meets the eye," Ortner said. "I don't think the first quarter of economic growth is anything to crow about. The second quarter should do somewhat better than that, although I think it will be sluggish, too."

President Reagan said during a Rose Garden ceremony yesterday that, despite the ominous economic signals, America is in "good economic health . . . As summer follows spring, inflation will remain low and our economy will continue to grow, creating still more jobs."

Consumer spending unadjusted for inflation rose 0.7 percent in April, reversing a 0.2 percent decline in March and suggesting to some economists that consumer spending will continue to support the economy during the second quarter.

However, when that figure is adjusted for inflation -- as it will be in a report to be released next month -- real spending should be much lower, economists said. In addition, it probably will not continue to rise at a faster pace than the increase in income, economists said.

The 0.7 percent increase in consumption is "not the world's greatest rate," said Alan Murray, an economist with Citibank Information Services.

Personal consumption expenditures for the first three months have been relatively flat, suggesting that the worsening trade deficit and low inventory buildup could pull gross national product for the first quarter down into negative numbers.

"It wouldn't take a great deal of change" for the first-quarter GNP figure to be negative, Murray said.

Disposable personal income -- income after taxes -- jumped $76.7 billion in April, compared with a $9.3 billion decline in March, attributed in large part to delays in payment of federal income tax refunds. Excluding the delays in tax refunds, disposable personal income rose $11.3 billion in both March and April, Commerce said.

The business economists said that a recession in 1986 would last only six months, compared with the 16 months of the most recent recession. "We see this as an adjustment problem caused by the high trade deficit and the budget imbalances, not a sharp recession," said Ben Laden, president of the association.

Laden also said that, because of the recession, the federal budget deficit, forecast at about $165 billion in fiscal 1987, could rise to about $300 billion in that year. The Fed's discount rate cut would not be enough to avert a recession next year, Laden said.

"We also need a lower dollar and evidence that growth is picking up in other countries," Laden said. "If those things happen, then we could get through next year without a recession."

The business economists forecast inflation this year would be about 4 percent, with the unemployment rate dipping only to 7.2 percent from the 7.3 percent rate last month.

Real growth this year would be 2.9 percent, compared with the 6.8 percent rate last year. The Reagan administration is forecasting growth of 3.9 percent for this year.