With truck stops across the country low on diesel fuel and prices reported as high as $1.13 a gallon, the nation's truckers warned yesterday that a widespread economic slowdown may result unless supplies are increased.

One group, the Independeant Truckers Association, sent 28 big rigs into Washington in the predawn darkness yesterday to double-park in front of the White House Association President Mike Parkhurst warned that a massive convoy will be sent to tie up Washington trafflic unless the trucker's demands are met.

"This was just a little landing party . . . to kind of let people know the trucks are out there," Parkhurst said of yesterday's incident. He said his organization represents about 30,000 independent truckers.

Representives of another group, American Trucking Associations Inc., met yesterday afternoon with U. S. Energy Secretary James Schlesinger to explain the problems.

"If the trucking industry is slowed down because of the unavailability or the high price of fuel, there will be a ripple effect that can cause a nationwide economic slowdown," ATA Vice Chairman Frank E. Cochran said in a press conference before the meeting with Schlesinger.

"Supplies are getting tighter each day, and we think we're on the verge of a national crisis," said Earl Hoekenga, president of Ryder Truck Lines, at the press conference.

Schlesinger told these and other trucking and truck stop industry representatives during a one-hour meeting that diesel shortages may be "slightly alleviated" during the next six months, in the words of a spokesman for Schlesinger.

The spokesman said much of the meeting focused on high prices rather than supply, with the representatives complaining of 30-cent-a-gallon increases this year.

An Interstate Commerce Commission officials at the meeting said the ICC is considering allowing a passthrough of fuel costs to customers by an increase in federally regulated trucking freight rates, the spokesman said.

Officials of the ATA said they do not support the ITA's threat of a convoy to Washington. ATA represents trucking companies and is often in disagreeement on issues with the ITA representing independents.

But yesterday both groups joined in demanding that truckers be granted all diesel fuel they need for the nation's roughly 300,000 long-haul trucks.

Diesel fuel for trucks, most of which is sold througt truck stops on major highways, has been slightly shorter supply that gasoline during the current shortage, in part because farmers are entitled to all they need for their equipment.

Truckers hauling fresh farm produce are also entitled to all they need, but industry representatives said as a practical matter it is nearly impossible for a truck stop operator to discriminate amont truckers in this way when there are long lines at his pumps.

Long lines have been reported at many trucks stop across the country. There are also limits on purchases and some truck stops are entirely out of fuel, industry representatives said.

The American Movers Conference, representing the interstate moving industry, reported shortages mostly in the west and midwest yesterday. A news release reported diesel prices ranging from 68 cents a gallon in Las Vegas to $1.13 in Louisiana. Unlike gasoline, diesel is not subject to federal price controls at the pump.

O. V. Jarrel, whose truck stop north of Richmond is one of the nation's busiest, said he could sell twice as much diesel if it were available. He said Texaco, his major supplier, recently cut his allocation to 80 percent of what he sold during the same month last year.

An industry spokesman said after the Schlesinger meeting yesterday that the representatives there felt the secretary was "sympathetic and understanding to our problems." They were told diesel supplies would be about 90 percent of what would be used under normal conditions, the spokesman said.

But Schlesinger's own spokesman said the secretary warned the industry representatives that the country's stocks of home heating oil - essentially the same product as diesel fuel - are the lowest in four years and must be rebuilt before next winter. CAPTION: Picture, ATA'S FRANK E. COCHRAN . . . foresees "ripple effect"