LIMA, Peru — In this seaside capital, the tales of graft were multiplying like the potholes.

There was the unfinished highway to the airport that had left a trail of indictments and protected witnesses instead. There was the light rail line that prosecutors say was built with $8 million in bribes.

Not even the statue of Christ the Redeemer standing above the ocean was untouched: It was donated as a gift by the Brazilian construction giant that had doled out the bribes.

The company, Odebrecht, has been at the center of Latin America’s biggest corruption scandal in a generation, with government officials jailed in Ecuador and Brazil and dozens under investigation in Venezuela and Colombia.

In Peru, the scandal may be taking down its biggest figure yet: President Pedro Pablo Kuczynski. Peru’s Congress is set to open impeachment proceedings against Mr. Kuczynski on charges that he improperly received $782,000 from Odebrecht through a company he owned. The president admits to receiving the money but says he did nothing wrong.