WASHINGTON — The House Oversight Committee on Monday announced an investigation into 12 pharmaceutical companies and their drug-pricing methods, billing it as one of the broadest inquiries in decades into how drug manufacturers set prices.

It is the fulfillment of a pledge from Rep. Elijah Cummings (D-Md.), the committee chairman, who has said he will make high prescription drug costs a top priority in his oversight agenda. One of the committee’s first hearings, set for Jan. 29, will focus on the same topic.