Housing starts rose again last month to their fastest pace so far this year, but analysts said the upturn was only an adjustment and did not change forecasts that the economy is entering a moderate recession.

Commerce Department figures showed the number of new dwelling units begun in June at an annual rate of 1.935 million units, up 5.7 percent from the revised 1.83-million-unit pace in May, and the second monthly rise in a row.

Although the June performance was the strongest so far this year, analysts said the mild rebound did not alter forecasts that a recession probably is at hand. The June level still was 8 percent below that of a year ago.

Kenneth Biederman, chief economist for the Federal Home Loan Bank Board, said the developments only show that in the wake of recent moves to bolster mortgage lending, "it's possible to have a recession without a big slump in housing."

Biederman said the June pace was in line with earlier predictions. Residential construction has strengthened moderately after plunging to a low of 1.381 million units in February.

The statistics came as top Carter administration officials continued to press Congress not to "overreact" to predictions of a 1979-80 recession and to hold off any decision on whether to enact a tax cut.

At a meeting of the House Budget Committee, Treasury Secretary W. Michael Blumenthal told panel members it would be "a grievous mistake" to try to "finance" the recent rise in oil prices by relaxing monetary or fiscal policy.

"It would be just running the printing presses," Blumenthal said.

The Treasury secretary, who only weeks ago was designated President Carter's chief economic spokesman before this week's White House shakeup, was accompanied by Budget Director James T. McIntyre.

The two were challenged by liberals, who asserted some action was needed to stave off recession. But Blumenthal insisted repeatedly: "The numbers...do not indicate that any action is needed now."

The June gain in housing starts again was concentrated in apartment units. Construction starts of multi-family units rose to an annual rate of 528,000 in June from 482,000 in May.

Starts of single-family units surged to an annual rate of 1.28 million units from 1.23 million the previous month. Activity was strongest in the South, $&(WORD ILLEGIBLE with continued softness in the Western states.

At the same time, the number of new building permits issued - a key barometer of construction trends - rose 2 percent in June to an annual rate of 1.647 million units, still below that for June 1978 by 17 percent.

Despite the widespread increases, economists predicted that June would prove the peak of the housing revival this year, and that starts would begin dropping again in the next several months.

Michael Sumichrast, economist for the National Association of Home Builders, suggested that the June rate could prove to be "a statistical fluke due to a very large number of previously unused building permits."

There were some indications earlier that construction activity in the earlier part of the year had been depressed artifically by the combination of bad weather and the impact of the Teamsters' strike. CAPTION: Picture, Treasury Secretary W. Michael Blumenthal during testimony on Hill yesterday. By James K. W. Atherton - The Washington Post; Graph, Housing Starts, The Washington Post