Treasury Secretary Donald T. Regan said yesterday that if the growth in federal spending were reduced to 1.5 percent a year, the federal budget deficit would drop from just under 5 percent of output now to around 1 percent.

Regan, in an address to the Detroit Economic Club, said his projection depended on a 4 percent inflation rate and a 4 percent annual rate of growth of gross national product.

"These low spending growth rates are achievable given the political will and continued noninflationary growth," he said. "With inflation continuing low, there is ample room for interest rates to fall and for interest outlays to come down."

However, to achieve a 1.5 percent annual increase in spending with higher growth planned for the defense budget and the steadily increasing share of the budget taken up by interest on the debt, entitlements and other programs would have to be slashed dramatically, budget analysts have said.

Regan did not address specific budget cuts in his address.

"With growth continuing strong, employment will rise and poverty will fall," Regan said. "The fairest way to reduce federal spending on the social safety net, the way we would all applaud, is for the unemployed and the poor not to require such aid because they are back at work, no longer in poverty and sharing fully in the general prosperity."

"That is the single best way I know to control spending," Regan said. "Indeed I have to confess to you it's the only lasting way I know."

Regan said that if 4 percent real growth is maintained every year, federal spending would fall as a percent of output by one percentage point every two years. By 1989 federal spending would decline from about 24 percent of GNP last year to about 21 percent of GNP by 1989, and tax revenue would increase to a little under 20 percent of GNP from just under 19 percent last year.