President Carter, beginning a two day cross-country trip, promised the water-source West tonight that a crash program of energy development will not usurp state control of water resources.

Arriving here for a dinner meeting with western governors, Carter issued a prepared statement designed to ease fears among westerners that federally directed energy programs will lead to exploitation of their region's water and other natural resources.

"With the exception of unique federal and Indian water rights, the states must allocate their water resources in the manner best suited to themselves," he said.

From the airport, the president went immediately to a dinner meeting with eight governors, members of the 10-state Western Governors' Policy Office, where energy policy and the West's role in developing it was the major topic.

Carter's trip, although officially "nonpolitical," was designed to bring him in touch with two of his most skeptical political constituencies -- western state officials and organized labor.

On Thursday, the president is to fly to San Diego and address the convention of the AFL-CI0 Building and Construction Trades Council. Organized labor has been among the sharpest critics of administration economic policies and is widely viewed as preferring Sen. Edward M. Kennedy (D-Mass.) to Carter as next year's Democratic presidential nominee.

As for the West, Carter has never enjoyed widespread support in this region, and he deepened suspicions of his intentions early in his administration with an attempt to kill a number of western water projects. now there is concern in the West over the likely impact of the administration's proposed energy program, which would rely heavily on synthetic fuels manufactured from coal and other resources of the region.

Reflecting this concern, the Western Governments Policy Office recently adopted a resolution calling for phased, rather than crash, development of synthetic fuels.

The governors also favor increased federal aid to the region similar to what has been provided to eastern coal mining regions by the Appalachian Regional Commission.

In his prepared statement, the president sought to reassure the West on the subject that has caused him the most political trouble in the region -- water.

While reiterating his call for enactment of the energy legislation, including the creation of an energy mobilization board with power to bypass state and local regulations, Carter said:

"I strongly believe that we must preserve the essential and historic role of the states in the process of allocating water among competing needs. I have and will continue to support legislative language to make it clear that federally supported energy development should be accomplished without preemption or change of state water laws, rights, or responsibilities."

The president added that "when the issue is priorities of water use in a state, the state must and does have the ability to say no through existing state water-allocation systems. This right must and will be protected in the energy proposals now pending before the Congress."

Carter was greeted at Kirkland Air Force Base near here by about 3,000 people, including a high school band and cheerleaders. In sunny, 80-degree weather that contrasted sharply with the snow and cold he left behind in Washington, the president told the crowd he is convinced the country can achieve a stable and growing economy while preserving the "quality of life" of the West and other regions.