Sales of new single-family houses rose 22 percent last month, the biggest monthly increase in more than four years, the Commerce Department reported yesterday.

An obviously delighted President Reagan immediately predicted that further declines in interest rates will lead to even better days ahead.

Reagan told the U.S. League of Savings Institutions yesterday that "I do believe the financial markets are beginning to understand the depth of our commitment to a fight against inflation. This means interest rates should drop still further in the days ahead, and all those interest-rate-sensitive activities like homebuilding and car buying will pick up and gather new strength," he said.

"A few months ago, I went out on a limb with the prediction that we'd see interest rates drop again before the end of the warm weather. Well, we've had a beautiful Indian summer. Last week, Friday, the temperature here in town hit 75 degrees and the prime fell to 12 percent," he said.

The president spoke by telephone hookup to the league's annual convention, meeting here in the Washington Convention Center. His remarks echoed those of Treasury Secretary Donald T. Regan, who told the thrift industry trade group Monday that "the economy will remain buoyant but not overheated" and will grow at about 4 percent through 1985.

The house sales data showed new houses selling at an annual rate of 679,000 in September, up from 557,000 in August. The September figure was 14 percent above the same month a year ago and the best showing since May of 1980.

Most analysts attributed the jump to the rapid decline in interest rates that has taken place since the end of July. Rising rates through the spring had raised considerable alarm in the housing industry, but the surge peaked in July, and many economists see further improvement at least into the first part of 1985.

Mark J. Riedy, chief economist of the Mortgage Bankers Association of America, said that he foresees "interest rates coming down in 1985 at least through the first half of the year" for a number of reasons, including the fact that "inflation has been good for a couple of years and the prospects for inflation are good for the reasonably foreseeable future. Secondly, the economy is slowing down, and that reduces the overall demand for credit in the private sector. . . . "

Riedy also said that the "size of the federal deficit could shrink relative to the growth of GNP and relative to the growth of private savings," providing a "better balance between" private savings and the deficit.

Kent W. Colton, executive vice president of the National Association of Home Builders, predicted "over the next six to eight months you should see a modest decline in interest rates," with mortgage rates in the range of 13 percent.

However, others pointed to the fact that the Commerce figures were based on actual sales of only 55,000 units and that seasonal adjustment factors supply a lot of leverage that can cause the annualized rates to jump around quite a bit.

Of the units sold, the median price was $80,000, and the average price was $100,000. So far the actual total for the year is 506,000, an increase of 6 percent over the 1983 pace.