With turnout at under 20% of registered voters, incumbents U.S Senator Mike Lee, U.S. Reps John Curtis, Burgess Owens and Blake Moore, and State Rep Kera Birkeland were all leading their challengers in seeking a spot on the November ballot.
The Salt Lake Tribune projected Lee would win his race.
Summit County Clerk Eve Furse said her office would release updated vote counts later Tuesday night.
Wasatch County results are not yet available.