Gov. Charles S. Robb, citing for the first time a $64.4 million shortfall in state income tax revenues, today ordered a 1.5 percent across-the-board cut in state spending--the third budget reduction the governor has demanded in less than two years.

Robb also took a variety of other administrative steps to save money, including a freeze on overtime and some construction projects. He urged the General Assembly and judiciary to also cut their budgets by 1.5 percent.

The latest cut in state spending comes on top of a 5 percent cut ordered by Robb in the 1982-83 fiscal year that ended last June and another 6 percent already in effect for the current fiscal year.

The impact on state aid to local governments and schools would be minimal if felt at all, Robb said, because officials now project a larger than expected increase in sales taxes of $41.7 million, one-third of which would go to local governments.

"The net effect is a hardship on the state," said Robb. Cuts would tighten expenditures in such areas as the governor's own offices, a broad range of commerce and human resources agencies, transportation and public safety.

In an appearance before key tax committees of the General Assembly, Robb blamed much of the projected shortfall--including a falloff of $95.3 million in state income tax revenues--on "the tenacity of the deepest recession since World War II." The income tax is the largest source of revenue for the state.

Robb also said the lower rate of inflation, which has kept prices and income down, and changes in state and federal tax laws have all helped lower projections for the second year of the state's $13.7 billion biennial budget.

Robb won general support today from Republican and Democratic leaders of the General Assembly, although they stressed that they expected some state agencies to be exempted from the cuts, including those for mental health, corrections and state police.

Robb agreed that some agencies may be spared, but declined to identify them.

"He's only set a broad outline, I will be especially interested in the details," said Del. Richard M. Bagley (D-Hampton), chairman of the House Appropriations Committee.

Several legislators have privately expressed concern about how far the state can go in reducing expenditures before considering any general tax increase.

Legislators generally agree that no tax increase is expected this fiscal year, but Bagley said it was too early to tell whether the General Assembly, when it convenes in January, would have to consider an increase for the 1984-86 biennial budget.

In a 20-minute speech before the Senate Finance and House Appropriation committees, Robb suggested "it might have been easier to delay any announcement" of the cuts "until after the General Assembly elections" on Nov. 8.

"But I don't believe . . . that delayed action would be consistent with Virginia's tradition of painstaking, cautious financial managment," Robb said.

Robb said he made the announcement now because it was "easier to spread (the cuts) out over a nine-month period" until the end of the 1983-84 fiscal year and "cushion the impact" rather than possibly make bigger cuts later.

Representatives of local governments and higher education, who objected to the previous cuts and in some cases successfully lobbied for changes by the legislature, also generally backed Robb today.

"I'm sorry we have to make a cut," said Dr. Gordon K. Davies, executive director of the state Council on Higher Education. "The cuts appear to be applied equitably. We'll take our share and no more."

Davies said the cut in the $500 million higher education budget probably would be absorbed by reductions in supplies and equipment and allowing vacant positions to go unfilled. He said it was too late into the academic year to affect faculty positions or the number of courses offered.

A spokesman for the Virginia Municipal League, which earlier this week urged a one-cent increase in the state sales tax to be applied to local education, said his group would not likely object to the cuts because "they were not laid squarely" on municipalities. "We could and should do our part," said league executive director R. Michael Amyx.

Robb order the latest budget cuts despite higher than expected revenue collections for July and August, the first two months of the current fiscal year. Robb said the overall projection for 12 months would still be only 9.4 percent in revenue growth compared to 11.1 percent originally projected.

For personal income taxes, Robb said the growth rate is now expected to be 10.4 percent, up from last year's increase of 7.3 percent, but still significantly below the 16.6 percent used to originally balance the current budget.

Robb said the projected shortfall also will be partially offset by a surplus of $39.6 million from the previous fiscal year. Much of that money-- $27.9 million--was found earlier this week after an accounting error was discovered in the state's capital budgets. However, Robb indicated that much of the money already was target for specific projects.