An increasingly violent nationwide strike by independent truckers continued to grow yesterday, causing serious disruptions of food and fuel deliveries amid signs that President Carter was preparing to give in to their demands for more fuel.

Dozens of truckers defying the work stoppage were shot at or stoned while driving on highways in at least 20 states yesterday, while agriculture officials in several states warned that entire crops were in danger of rotting because farmers were unable to get them to market on trucks.

In the most violent day of the strike, which has been growing sporadically for more than a week, truckers continued to protest over fuel prices, supplies and federal and state regulations that they say unfairly inhibit their business.

Reports from several states indicate that the effects of the strike are now being felt almost everywhere.

The household moving industry is facing a virtual shutdown. The American Movers Conference, the largest household goods-movers trade association, reported yesterday that more than half of the estimated 50,000 trucks were off the road and the rest could be by the weekend.

AMC spokesman Steve Cloud said, "We are close to a total shutdown . . . It's a very shaky situation . . . Most of our drivers fear violence."

Cloud said that this is usually "our peak season," and indicated that between 800,000 and 1 million persons move during the summer.

Meanwhile, Interstate Commerce Commission spokesman Tom Davis reported that tank trucks, which carry increasingly scarce fuel supplies to consumers, are "90 percent down in the southeast and 100 percent down in New Jersey," with other areas less seriously affected.

Davis also said that 65 percent of all refrigerated carriers have been taken off the road, meaning many perishable crops are unable to get to the market.

In a White House news conference yesterday afternoon, President Carter called for an end to the interruption of the delivery of food and fuel, and deplored the violence that has occurred.

Carter said that before he leaves for Tokyo tomorrow he will announce measures to meet "legitimate grievances" enunciated by the truckers.

Appearing with FBI Director William Webster and Assistant Attorney General Philip Heymann, Carter said he wanted to stress, "in the strongest possible terms, that violence and lawlessness will not be tolerated. Murder, vandalism and physical intimidation are criminal acts and will be treated as such."

Carter said he had received an FBI report that he requested on the death of a trucker in Alabama Wednesday. Webster said the FBI had authority to enter that investigation because of indications of a violation of the Hobbs Act, which makes illegal violence or threats of violence aimed at interfering with travel on interstate highways.

"The full resources of the Department of Justice will be used to assure that order is preserved, violators apprehended and the individual rights of citizens protected," Carter said.

The truckers are demanding increased diesel fuel supplies, and there are indications that Carter will end special allocations of diesel fuel to farmers and shift some of that supply to the truckers.

But it is unlikely that the president can or will do anything about state regulations concerning weight and length restrictions. Truckers want all states to allow 80,000-pound trucks and rigs up to 60 feet long on their roads. Some Midwest and Delta states have lower weight limits for safety reasons, while some East Coast states limit truck size, for the same reasons.

The Carter is also probably not going to allow truckers to drive faster than 55 miles per hour. They want a 65 mph speed limit.

A leading food industry spokesman urged quick action by Carter. Food Marketing Institute President Robert Aders warned in a telegram to the White House that further delays "could lead to (nationwide) shortages of meat and fresh produce within days."

But there was little indication that truckers were heeding the warnings from the White House.

In New Orleans, about 200 independent truckers voted to take their rigs off the road, doubling the number of strikers there and prompting a management warning that the Port of New Orleans - the second-largest in the nation and the biggest industry in the city - could be seriously affected.

Elsewhere, truckers have blocked 36 truck stops in New England, according to Oscar Williams Jr., a spokesman for the Independent Truckers Association.

Some 40 truckers have virtually closed the Chelsea, Mass., New England Produce Center, one of the region's main sources of fresh fruit and vegetables. It took the arrests of some dissident truckers and a police escort so convoys of strike-breaking truckers could be led from that market yesterday.

In the South, Georgia Agriculture Commissioner Tommy Irvin warned that the state's peach and watermelon crops were "in serious jeopardy." Orchard owners have stopped harvesting in the hopes that their peaches will keep better on the trees than sitting in wagons.

Florida Department of Agriculture marketing director John Stiles said, "We're running real tight.We've got to get sweet corn, watermelon and tomatoes moved by Monday. Nothing's spoiled yet, but it's close."

Stiles said his state needs about a thousand trucks "as soon as we can get 'em." Florida Gov. Robert Graham declared a state of emergency yesterday because of the strike's success in tying up his state's fuel supplies.

John Mohay of the National Independent Meat Packers Association said 75 percent of all shipments to the East Coast are not making it. "It's getting worse," Mohay said. "We can't get trucks."

One of his members was shot at three times while driving between the Midwest and New York, Mohay said, adding, "We've had cases of tires slashed at truck stops, air hoses being cut and bricks being dropped through windshields when trucks go under overpasses."

Alabama Gov. Fob James urged truckers to arm themselves and shoot back. "It's time to put the billy back in the billystick," he said. "I'd put a shotgun beside me and go . . . and I'd kill anybody that tries to stop me."