The Environmental Protection Agency has dropped its claim that an energy company contaminated drinking water in Texas, the third time in recent months that the agency has backtracked on high-profile local allegations linking natural-gas drilling and water pollution.

On Friday, the agency told a federal judge it withdrew an administrative order that alleged Range Resources Corp. had polluted water wells in a rural Texas county west of Fort Worth. Under an agreement filed in U.S. court in Dallas, the EPA will also drop the lawsuit...