This year's budget deficit will be $51 billion or $52 billion rather than the administration's first estimate of $55 billion, Treasury Secretary Donald T. Regan told reporters yesterday.

At a breakfast meeting with out-of-town editors and wire service reporters, Regan also linked an easing of inflation this year with sluggish economic growth for the next six months.

A smaller tax cut this year and next will likely shrink the federal deficit for 1981 and fiscal 1982 despite higher interest rates pushing up spending, Regan said.

He predicted a slowdown in the economy in the next six months and an improvement in inflation. Echoing a recent comment from Murray Weidenbaum, chairman of the Council of Economic Advisers, Regan said "hopefully, we've seen the end of double-digit inflation."

The administration's latest economic forecast, which will be published later this month, sees a flat economy in the April-to-June quarter, "a third quarter that may be negative, and then I think we're going to have a turnaround in the fourth quarter," Regan said.

Although optimistic about inflation, the Treasury secretary would not predict when interest rates would fall from current high levels. However, he did say that he expected the key prime lending rate, now at about 20 percent, to fall below 10 percent during 1982.

Unemployment, which jumped to 7.6 percent last month, may increase as the economy slows in the next few months, Regan said. But the administration "does not expect too much of a pickup," and he does not believe that the jobless rate will hit 8 percent, he added.

The slowdown in the economy "is to be expected in a fight against inflation," Regan said. But the downturn would not amount to a recession, he said. This is formally defined as at least two consecutive quarters of falling output. Unemployment figures for June, to be published today, will show a rise of "10ths of a percent" from the May 7.6 percent, Regan told reporters.

Present high interest rates are a side effect of the Federal Reserve Board's tight grip on the money supply, the Treasury secretary said. Administration officials have predicted that rates will fall sharply once the markets see Reagan's economic program in place. So far the financial markets have not responded to the president's budget successes of last week.

Regan said that as the Fed's tight money policy continues, inflation will come down and interest rates also will fall.

Such a fall would help hard-pressed industries such as autos and savings and loan institutions, the Treasury secretary added. He repeated the administration's opposition to a new tax-exempt savings bond to help S&Ls, saying that this would not be the best way of aiding the industry. Lower interest rates and deregulation would be better, he said.

Questioned about whether the Chrysler Corp. would seek new loan guarantees, Regan said, "I don't see it at this time." He added the corporation would "do very well if interest rates come down."

The administration is "very optimistic" that the combination of Republicans and conservative Democrats which enabled the president to win House approval of his budget proposals also will get Reagan's tax cut plan through Congress. So far the Democratic-controlled House Ways and Means Committee has agreed on a different tax cut. Regan said that "the question now is dimension" and pointed out that the Democratic bill is now larger than the administration's.

Meanwhile, the Commerce Department yesterday reported a 4.7 percent drop in construction projects completed during May. It was the largest monthly drop since April 1980. Public construction dropped by 9.9 percent while private construction fell 3.1 percent, the department said. Building of highways and streets was down by 18.5 percent in the month, despite the warm spring weather.

After adjusting for inflation, construction fell during 1980 from 1979 levels and has dropped further this year. High interest rates hit the building industry particularly hard.