The booming economy is continuing to create more jobs - and more inflation.

The Labor Department reported yesterday that more than 700,000 persons found jobs in June, pushing the unemployment rate down to 5.7 percent from 6.1 percent. It was the first time in almost four years that the jobless rate has been below 6 percent.

That same strong economic expansion also kept inflation at a high level. The department said wholesale prices rose 0.7 percent in June, about as fast as in May. That works out to a seasonally adjusted annual rate of 8.7 percent.

Administration economists expect the strong growth of recent months to taper off in the final months of the year. There is a lingering fear that the June reports of strong jobs gains and high inflation will encourage the Federal Reserve Board to boost interest rates even higher in its attempt to fight inflation.

If that occurs, administration policymakers fear, economic growth in the last half of the year could be choked off.

Food prices remained the villain in the June inflation, increasing 1.1 percent. But nonfood prices, which economists consider a better barometer of inflation, rose 0.6 percent. That is a little less than May's 0.8 percent, but still high.

And even though economists think food inflation will moderate substantially during the next six months, they fear that food price rises that have already taken place will be echoed in the industrial goods sector as workers receive large cost-of-living increases.

Charles L. Schultze, chairman of the president's Council of Economic Advisers, said the improvement in the unemployment rate over the first 18 months of the Carter administration has been "literally striking." Since January 1977, 6.4 million Americans have found jobs and the unemployment rate has fallen from 7.8 percent to 5.7 percent.

Schultze conceded that the size of the June drop - which has been matched or exceeded in only three months during the last 15 years - may be a statistical aberration. "I don't know that it is, but it may be," he said. But the continuing decline in joblessness "confirms" the continuing good news on the employment front, Schultze went on.

Only Thursday the administration released a major revision of its economic projections that forecast unemployment would be at 5.9 percent by the end of the year. If that is correct joblessness can be expected to rise in coming months.

But the president's economic advisers have consistently underestimated the improvement in unemployment and at the same time underestimated the nation's inflation problem. In the Thursday revision the administration upped its 1978 inflation projection from 6 to 7.2 percent.

Schultze, at a White House briefing yesterday, called the 0.7 percent June rise in prices of so-called finished goods ready for final business or consumer users "clearly too high."

He said the continuing high inflation, both at the wholesale and consumer price level, demonstrates the necessity "to pursue the administration's anti-inflation program vigorously."

After the Schultze briefing, presidential inflation counselor Robert S. Strauss announced that the nation's home builders say they plan to cooperate with the president's anti-inflation program and will try to hold the increase in new homes prices this year below the 11 percent average of the last two years.

The Labor Department said employment gains in the economy last month were widespread, with teen-agers and adult men faring slightly better than adult women.

A survey of nonfarm business payrolls, which is different from the survey of households used to compute the unemployment rate, showed a strong gain of 275.000 jobs.

The Labor Department said the unemployment rate for nearly all groups in the economy declined in June. For whites the rate fell to 4.9 percent from 5.2 percent, while for blacks declined to 11.9 percent from 12.3 percent. The rate for black teen-agers fe11 to 37.1 percent from 38.4 percent.

Schultze said that with unemployment down to 5.7 percent, overall economic growth is less likely to yield further large reductions. Instead, he said, the government must concentrate on specific programs aimed at helping groups, such as inner-city youths, with special job-finding problems.

Government analysts said that part of the improvement in the teen-age unemployment problem last month can probably be attributed to special youth programs.

While the improvement in unemployment is heartening, said Brookings Institution economist Arthur Okun. 'I cannot generate a lot of enthusiasm' on the inflation side.

Okun noted that productivity, or output per hour worked, has been declining steadily for the last year, pushing up the cost of doing business, and that wage gains appear to be accelerating.

"More people are getting employed," said Okun, a chairman of the Council of Economic Advisers in the Johnson administration, "but they seem to be producing less."

At the wholesale price level, costs turned up sharply for most meats, including beef, as well as for dried fruits and vegetables. After big 1.2 percent and 2.8 percent increases in April and May, prices for consumer durable goods such as cars rose only 0.2 percent.

The index for capital equipment, such as machinery, rose 0.8 percent after a 0.9 percent rise in May.

The index for intermediate materials, which are semifinished goods such as steel or flour, rose 0.3 percent, while the crude materials index of products like iron ore rose 1.7 percent.

The index of finished goods stood at 194.4 percent of its 1967 average last month, which means that a selection of goods costing $100 in 1967 cost $194.40 in June.