The Senator, through a spokesman, said the Mormons needed a new facility at Dugway because of the high number of church members at the base. ''Additionally, its remote location makes it impossible to have a facility adjacent to the base,'' he said. Dugway is about 35 miles from the nearest town.

Carl Roberts, head of the Mormon community at the base, said the church wanted a new facility to accommodate the expected expansion on the base.

Laurie Snow, a spokeswoman for Senator Garn, said that if the Army did not come up with a plan that was satisfactory, the Senator would ask Congress to order the Army to let the Mormons have a lease. Supply Warehouse Is Used

Officials at Dugway say Mormons there have been using a renovated supply warehouse for their worship as well as for various classes and special workshops. Technically, the Army-owned building can be used by any religion, but the Mormons use it exclusively, the officials said.

Protestants and Roman Catholics use the base's chapel for their services and Bible study programs, the officials said. Jews do not have special services on the base because there are few of them, the officials said.

The Mormons have put the Army in an awkward position at Dugway, according to the officials. On one hand, base commanders are obligated to make sure the religious needs of the community are met. That means the Army has to provide the necessary space for church programs. On the other hand, the base officials say Army regulations prevent them from leasing land to Mormons because buildings must be nondenominational.

Kathleen Whitaker, a spokeswoman for Dugway, said only Congress could change the rules.

''The Army regulations don't allow for a separate building for separate religious purposes,'' she said.