WASHINGTON—The Environmental Protection Agency is planning to tighten standards for four water contaminants that can cause cancer as part of a new strategy to toughen drinking-water regulation, the head of the agency said Monday.

The agency said it will start rulemakings to revise standards for two contaminants used in industrial or textile processing, tetracholorethylene and trichloroethylene, within the year. The EPA will follow that rulemaking by setting stricter standards for epichlorohydrin and acrylamide, which can...