LIMA, Peru — Lawmakers voted on Friday to begin proceedings that could oust President Pedro Pablo Kuczynski of Peru, the latest leader accused of involvement in a corruption scandal that has shaken some of Latin America’s biggest countries.

The dispute involves Odebrecht, a Brazilian construction giant, which last year admitted to paying roughly $800 million in payoffs in exchange for lucrative projects. That revelation set off a flurry of investigations by prosecutors and lawmakers, principally in Latin America, seeking to learn who was on the receiving end of the payments.

According to documents sent to Congress and released this week, Odebrecht paid $782,000 in advisory fees to Westfield Capital, a company Mr. Kuczynski owns. Most of the payments occurred between 2004 and 2007, while Mr. Kuczynski served as Peru’s economy minister and prime minister.

On Friday, lawmakers voted overwhelmingly to move ahead with proceedings next week that could remove Mr. Kuczynski from office, on the grounds that he is “morally handicapped.” They scheduled a hearing for Thursday, at which Mr. Kuczynski is expected to present a defense.