President Carter has decided to support construction of pipelines to carry coal from the nation's Western coalfields to the South, according to administration sources.

Carters decision, reached earlier this month, is expected to end a decade-long congressional deadlock caused by the battling between railroad and pipeline interests seeking the incrative rights to transport the coal.

The pipelines, which would be almost 1,000 miles long, would carry "slurry" coal - coal that has been crushed and then mixed with water to form a sludge - from the fields in Wyoming and Colorado to major power plants in Texas and Arkansas. The pipelines could cost up to $1 billion each.

The pipeline companies need a grant of eminent domain - the right to use private property - before they can construct the lines. Carter's decision supports legislation to grant the power of eminent domain on a case-by-case basis but does not choose between companies or routes.

"The question now is not whether to go for enabling legislation, but how to establish a decision-making process in which Interior, Transportation and the department of energy weigh slurry pipeline applications," a source said.

Hundreds of millions of dollars could ride on the outcome of Carter's choice of which department would have the lead in weighing applications for "certificates of public convenience and necessity" required to condemn private property for coal slurry pipeline rights of way.

A decision to place the lead in the department of energy would favor slurry development, while placing it in Transportation or Interior would very likely lead to restraints on slurry development.

At a May 20 meeting, Interior Secretary Cecil D. Andrus, Transportation Secretary Brock Adams and presidential energy adviser James R. Schlesinger Jr. agreed that one of their three departments should have central responsibility. Carter is expected to name the lead department next week.

"What we are trying to do is formulate a process to make slurry right-of-way decisions intelligently," an administration official said.

After the President select a lead department, the administration position is to be made public.

Slurry politics over the last three years have been slightly charged, piting coal companies, utilities and industrial construction giants such as Bechtel Corp. and Brown & Root Inc., against railroad interests, environmentalists and some Western states concerned about scarce water supplies.

Over 3,000 miles of coal slurry pipelines have been proposed in recent years.

One of the largest projects was offered by Energy Transport Systems, Inc. (ETSI), a combine made up of Bechtel, Lehman Brothers investment bankers and the Kansas-Nebraska Natural Gas Corp. to build a more than $750 million, 1036-mile pipeline from Gillette, Wy., to White Bluff, Ark.

ETSI's coal would serve the more than 1.3 million customers Middle South, has vigorously supported slurry pipelines, saying they are necessary to deliver the amount of coal needed for the Gulf Coast states to convert power plants now using oil and natural gas to coal.

The railroads will continue to make a major contribution to moving coat to the Southern states, but passing legislation to provide eminent domain for slurry is "one of those things that has to be done." Johnston said.

The Senate passed, and the House has marked up legislation reversing President Carter's proposal to place responsibility for coal slurry pipelines in the energy department instead of the Interstate Commerce Commission.

The Senate passed a slurry pipeline right-of-way bill in 1974, and the House is expected to pass one this year.