The natural gas crisis that has closed schools and factories in 17 states eased slightly yesterday as the pipelines suffering the most critical shortages stemmed their gas drain for the first time in more than two weeks.

Four major interstate pipelines serving the 12 states hit hardest by the shortage and the cold told the Federal Power Commission yesterday that pressure in their lines had begun to pick up, indicating that more gas was entering the lines than was being drawn off by customers. The four firms said it was not that they had more gas, only that fewer customers were drawing it.

The reports probably mean that homes won't begin to lose their gas heat, as was feared late last week when pressure was falling along the entire Eastern Seaboard.

At the same time, the reports did not mean that closed schools and factories would reopen any time this week.

One reason given by the pipelines for an easing of their crisis was the orders in 11 states that schools and factories be closed. The only natural gas being given to schools and factories unable to burn bottled gas, oil or coal in any of the afflicted states is to prevent pipes from freezing and furnaces from turning cold.

Still another reason the crisis has eased is that the winter storms and sub-zero temperatures of the weekend never went farther south than New England, Ohio and parts of Pennsylvania and New York. Weekend demands on natural gas pipelines in the South did not exceed their ability to fill them.

The four pipelines reporting better supply conditions to the FPC yesterday were Columbia Gas Systems, Transcontinental Gas Pipeline, Texas Eastern Transmission Co. and Southern National Gas co.

Columbia pipes to Ohio, Pennsylvania, New York, West Virginia, and Virginia. Transco serves the entire Eastern Seaboard between North Carolina and New York. Texas Eastern's pipelines take gas to communities along the Ohio River Valley, then on to Pennsylvania, New Jersey and New York. Southern feeds from Louisiana to Mississippi, Alabama Georgia and South Carolina.

The four pipelines told the FPC that in the last three days they had seen fewer instances where customers drew more gas than they were alloted, a practice that was at least partly to blame for falling pipeline pressures last week. The pipelines had told their biggest customers to take only enough to maintain delivery pressures, warning that violations would be reported to the FPC for possible legal action.

"Any time a major resale customer overruns after a warning, the staff will recommend that the commission investigate it," said Joseph Soltirs, the FPC's chief trouble shooter. "We can't tolerate overruns by large customers, given the situation we now have."

All four critically short pipelines were out shopping over the weekend. Columbia was understood to be canvassing in vain in Louisiana, Texas, Kansas and Oklahoma - where colder than normal temperatures have created shortages of their own for intrastate gas not subject to FPC price ceilings.

The FPC allows 60-day sales of this unregulated gas to be made to interstate pipelines at prices almost 40 per cent higher than regulated interstate prices. But only a handful have been made, because there is no surplus gas of any kind east of the Rocky Mountains.

President Carter's natural gas emergency bills, which will be debated again today in the Senate, extends the period for selling intrastate gas to interstate pipelines from 50 days to almost 180 dasy. Carter is asking for the extension to encourage producers to sell whatever new gas they find to interstate consumers at the higher intrastate prices.

The only U.S. surplus lies west of the Rockies, where warmer than normal temperatures prevail. But three bottlenecks face eastern pipelines wanting to buy western gas.

Only two pipelines cross the Rocky Mountains and they are too small and too busy to take on much new gas. A third and much bigger pipeline runs southeast from California to west Texas and east Texas and into the national network, but contracts with Texas pipelines often prohibit the commingling of intrastate and interstate natural gas.

This is the bottleneck preventing Southern National Gas Co. from moving the 100 million cubic feet a day it contracted last week to buy from Pacific Gas & Electric Co. At best, half that gas is understood to be moving through Texas pipelines to ease Southern's plight.

The most troubled of the eastern pipelines, Southern has also petitioned the FPC to buy half the 250 million cubic feet a day that Columbia Gas Systems bought from Canada 10 days ago.

In effect, Southern has said it has a greater need than Columbia for the Canadian gas, a position with which the FPC has some sympathy. The FPC's four commissioners met Saturday to discuss the petition, but postponed a decision pending further arguments by Southern.

The 125 million cubic feet of Canadian gas Southern is trying to get will not solve Southern's or any other pipeline's shortage. FPC Chairman Richard Dunham told Congress last week the eastern two-thirds of the nation needs between 300 and 500 billion cubic feet more than it has.