Governors of the western states likely to feel the greatest effects of President Carter's massive energy proposals met in Denver today to express their support for the president. But they asked that they participate in a partnership with the federal government in achieving the new energy self-sufficiency goals.

"The states must recognize the national interest and then carve out the role we must play," said Gov. Scott M. Matheson (D-UTAH).

"We serve notice clearly today that the price of cooperation is partnership in formulating energy development policies, Matheson said.

Governors from six western states and representatives of the governors from three others came for the meeting called hastily Monday after Carter announced that the heart of the nation's new energy programs would be development of of coal and synthetic fuels.

Virtually all of the nation's oil shale and much of its coal lie under the Rocky Mountains and upper plains states.

Eugene Eidenberg, a Carter aide and head of the White House energy task force, told the conference, "I commit our administration to working with you to provide the kind of impact assistance that will protect this special environment in the west."

Among the concerns facing western states in the center of what will likely be a multibillion-dollar synthetic fuels industry are scarcity of water, adverse effects on the environment, lack of adequate transportation and other public facilities and sudden disruption of the life styles of towns that would go from villages to industrial communities in a matter of a few years.

Under Carter's plan, 2.5 million barrels of fuel from oil shale, coal liquefaction and other domestic sources would be flowing by 1990.

Colorado Gov. Richard D. Lamm (D) referred to the energy crisis as "disruptive as depression and as dangerous as war," and said he and his fellow western governors have no intention of undermining the president's initiatives, which are still subject to significant change.

Thomas L. Judge (D) governor of Montana and chairman of the Western Governors Policy Office, said the govenors from the states to be most affected will seek a meeting with the president soon to determine the role of the states in energy development and to iron out the specifics of energy impact assistance to be sought as a result of the expanded mining of western resources.

Carter aide Eidenberg tried to allay the governor's fears about maintaining adequate water supplies for agriculture and public consumption in the wake of what would be significant demands for water from the sythetic fuel industry.

Water requirements "will be financed and will be met," Eidenberg told the governors. However, he declinced to commit the administration to full funding of western water projects, which had created friction between the west and the administration when Carter cut off funding for 30 such projects in 1977.

Other governors at the meeting included Democrat Bruces King of New Mexico, Republican Jay S. Hammond of Alaska and Democrat Arthur A. Link of North Dakota. Representatives from the offices of the governors of Arizona, Nevada and Wyoming also attended the 2 1/2- hour conference.