The government's main gauge of future economic activity rose 1.5 percent in April, the sharpest increase in nearly three years and a strong indication that economic growth will begin accelerating this summer.

The index of leading economic indicators has risen strongly for three consecutive months, increasing 0.9 percent in March and 0.8 percent in February, the Commerce Department said yesterday. The April rise was the steepest since a 1.9 percent increase in June 1983.

President Reagan, speaking to the National Association of Manufacturers, said that the three months of increases in the index were "all signalling good times ahead."

Commerce Secretary Malcolm Baldrige said economic growth may be slow in the current quarter. "But with lower interest rates, lower inflation and a more competitive dollar, the economy's pace should accelerate during the second half," Baldrige said.

The index is intended to predict economic activity in the next three to six months.

Economists said that although the indicators suggested a more robust second half of the year, manufacturing still has not rebounded from its recent doldrums. One area in particular, the oil and gas industries, is suffering from the sharp drop in the price of oil, which has made it unprofitable to produce domestic supplies.

Economists had been waiting for several months for the decline in oil prices and interest rates to pump up the economy. Now many say that the economy should bounce back to a growth rate of about 4 percent, up from the 3.7 percent rate in the first quarter and what economists believe is a still slower pace in this quarter. The most notable improvement has been in housing sales, which have been growing at record levels recently.

In a separate report, the Labor Department said that the productivity of American workers climbed 3.6 percent in the first three months of the year, largely because of the strongest increase in output of goods and services in almost two years.

Nonfarm business productivity increased 4.5 percent in the first quarter, the best performance since the second quarter of 1984, Labor said. Higher productivity generally helps keep down prices because workers are able to produce goods more efficiently.

"I think it's a good sign for the economy," Martin Mauro, senior economist for Merrill Lynch Economics, said of the leading-indicators report. "The advances in the past couple of months have been unbalanced," with strong activity in the financial components of the index such as stock prices and money supply. "But the real-sector components have been falling. April numbers suggested strength in housing and autos, but not elsewhere in manufacturing," he said.

"Eventually, the strength in housing and autos will work its way through to other sectors," Mauro said. "Manufacturing has not responded to the dollar's decline, because it has not fallen sharply against all currencies and import prices have not risen strongly."

The indicators that contributed positively to the index were: money supply, change in credit outstanding, new orders for consumer goods, stock prices, net business formation, initial claims for state unemployment and building permits.

Those that negatively influenced the index were: average work week, contracts and orders for plant and equipment, and sensitive-materials prices.

The decline in the average work week and orders for plant and equipment are closely linked to activity at factories, economists said, and the continued decline of those measures suggested that manufacturing is not expected to rebound in the next few months.

"Most of the strength in the leading indicators was coming from financial measures . . . rather than activity in the real side of the economy," said Wharton Econometrics senior economist David Berson.