Merck & Co. will eliminate up to 13,000 jobs, about 14% of its work force, in the latest cost-cutting effort by a big drug maker coping with an aging product lineup.

The drug giant said the layoffs would be in addition to some 17,000 job cuts already planned and would cut spending by an extra $1.3 billion when finished at the end of 2015. Also contributing to the savings are the closings of unspecified offices and manufacturing plants.

Merck...