CHICAGO, June 4 (Reuters) - Lean hog futures dropped to their lowest price since January at the Chicago Mercantile Exchange on Tuesday as weakness in the Mexican peso fueled worries over demand in the biggest export market for U.S. pork, traders said.

The Mexican peso extended losses for a second day after a strong election victory for Mexico's ruling party sparked concerns about disputed constitutional reforms.

Ups and downs in ham prices adjusted for exchange rates correspond with ups and downs of U.S. pork sales to Mexico, Steiner Consulting Group said.

"Suddenly U.S. pork products became more expensive," the firm said. "As the price goes up sales decline, assuming steady demand."

CME July hog futures ended down 2.35 cents at 93.925 cents per pound and hit their lowest price since Jan. 23 at 93.650 cents per pound.

U.S. meatpackers slaughtered an estimated 481,000 hogs, up from 475,000 a week ago and 469,432 a year ago, according to the U.S. Department of Agriculture.

The department priced the pork carcass cutout at $100.76 per hundredweight (cwt), a drop of $0.67 from Monday. Belly values tumbled by $10.31.

Concerns about weak values for pork bellies and hams added pressure on futures, traders said.

"Fresh pork values have stopped going up and processing items so far have failed to pick up the slack," Steiner Consulting Group said.

Cattle futures also slumped.

CME August live cattle closed down 0.425 cents at 178.450 cents per pound. The decline reversed gains from Monday, when the contract bounced after hitting its lowest price since May 16.

CME August feeder cattle settled down 0.175 cent at 256.025 cents per pound.

Wholesale boxed beef prices rose for choice cuts and select cuts, according to USDA data. (Reporting by Tom Polansek in Chicago; Editing by Alan Barona)