The Virginia State Corporation Commission ordered a two-week cutoff of natural gas supplies yesterday to industries, some schools and other non essential agencies in the heavily populated eastern section of the state in an effort to conserve dwindling gas supplies for home heating.

The gas curtailment, announced by Gov. Mills E. Godwin, was the first such drastic move in this area, as extreme cold continues to cripple major portions of the United States. Virginia officials estimated the gas shut-off could lead to layoffs of about 30,000 workers.

In a separate report issued by Godwin at his Richmond news conference, official said that about one-third of Virginia's 1,700 schools have already been closed because of fuel shortages and cold weather. How many additional schools would shut down because of the gas cutoff was not immediately announced. Officials said about 10 per cent of the state's schools rely on natural gas heating.

The emergency moves in Virginia were announced as a three-day thaw that melted ice and brought mild mid-day weather to the Washington area appeared to be nearing an end.

The National Weather Service has predicted that bitter cold will return to the area tonight, with evening temperatures dropping, to about 15 degrees in the city and to 5 degrees in parts of the suburbs. Up to an inch of snow is forecast for Western Maryland and northwestern Virginia today, but snow is not expected in the Washington area.

The frigid weather, driven by an Artic cold moving in from Canada and the Dakotas, is predicted to chill the Washington area at least until early next week.

The unusually frigid winter across much of the United State led yesterday to the closing of all public and private elementary schools in Pennsylvania, where 2.6 million youngsters are enrolled. Gov. Milton J. Shapp asked the Carter administration to divert natural gas supplies to Pennsylvania from other parts of the United States.

The Baltimore Gas and Electric Co., which serves much of Maryland including parts of Montgomery and Prince George's counties, warned yesterday of possible curtailments of gas supplies to industries over the coming weekend. It noted such cutoffs could lead to temporary layoffs.

While Ohio has become the state hit hardest by the winter energy crisis, the effects of the cold remain widespread. In Delaware, the Delmarva Power and Light Co. announced a halt of gas supplies to its 20 biggest industrial customers. Wisconsin Gov. Patrick J. Lucey ordered heat turned down to 63 degrees in most state buildings. Equitable Gas Co. has asked schools to close in eight West Virginia counties.

In Buffalo, N.Y., the Erie County Recreation Department postponed its annual winter carnival because of near-zoo cold.

Godwin's announcement of Virginia's emergency steps yesterday was accompanied by grim words and statistic. A total of 3,163 Virginia homes were reported already to be without heat, mainly in the Norfolk area.

"I think it is my duty as the chief executive of the commonwealth to talk plainly to the people of Virginia about the energy situation we are facing," Godwin asserted as he announced what he described a "some drastic steps."

The State Corporation Commission's order will cut off natural gas to industries, schools and some government agencies in the area running south from Fredericksburg to the North Carolina border and generally east of Interstate 95. The section includes the Richmond-Petersburg area where 6,000 Allied Chemical Corp workers will be laid off, and the Hampton Roads area in southeast Virginia where an estimated 20,000 industrial jobs may be affected.

Godwin said that natural gas service would continue only to homes and establishments serving "essential human needs." Hospital, day-care centers, nursing homes, colleges, prisons, and water and sewage treatment plants would still receive gas supplies. The State Corporation Commission said it had taken its action because Commonwealth Natural Gas Corp., which supplies natural gas to six Virginia distribution companies, was running critically short of gas supplies for the state. Without the two-week cutoff, the state would not have enough gas to heat homes for the rest of the winter, SC official said.

Although Northern Virginia was not affected by the gas curtailment, state officials said they will monitor gas supplies to other parts of the state and may undertake some further action next week, possibly to divert gas supplies from one section of the state to another.

The city of Danville, in southern Virginia, which is supplied by another gas pipeline, appealed to Godwin yesterday to ask the President to declare the city a disaster area because of a threatened cutback in the city's gas supplies. Godwin responded by saying he would probably take such action later. If granted, it would make the city eligible to apply for emergency unemployment benefits and Small Business Administration loans from the federal government.

President Carter has already declared parts of Virginia and Maryland as disaster areas, permitting an estimated 5,300 seafood industry workers to seek unemployment benefits and low-interest loans. The Virginia Employment Commission said yesterday that its representatives would be flown Monday to Tangier Island off the Virginia coast in the Chesapeake Bay to accept applications from watermen seeking unemployment aid.

As emergency measures were adopted across the nation, Washington basked yesterday in its third day of pleasant, sunny and mild winter weather. The temperatures recorded at National Airport rose to 43 degrees at mid-afternoon - a level that has usually been considered normal for this season.

Washington's apparently transient thaw - which is expected to continue only through part of today - was greeted with relief and some delight.

By midafternoon, ice clinging to the base of Alexander Hamilton's statue outside the Treasury Department building had loosened enough for James Waterman to begin chipping it off with a shovel. "I did some yesterday, too - it was easy to get up," said Waterman, a National Park Service grounds maintenance worker. "I know the sun's doing some of the work."

Like a number of others in Washington, FBI agent Ray Connolly strolled out of his office yesterday without his overcoat. "It seems like spring," he remarked.

But many sensed that mild weather would not last. Thomas Scheren, who manages the National Sculpture Garden Ice Rink, described Washington's recent icy weather as a misfortune both for skaters and for workers who must keep the rink in shape. He had also heard a forecase of a possible new snowfall here. "I hope not," Scheren said. "I hate snow."