WASHINGTON—The U.S. unveiled a new series of sanctions on Moscow over a nerve-agent attack on a former Russian spy and his daughter in the U.K., in a rare direct confrontation that could escalate into a broad series of diplomatic and economic measures between the two countries.

The U.S. announcement Wednesday included an additional threat to follow through with a second round of measures in 90 days’ time if Russia doesn’t meet a list of three criteria.

The...