Susana Villaran, a leftist and the first woman to hold the mayor's post, in 2013 faced the recall vote halfway through her four-year term.
Odebrecht's former Peruvian boss Jorge Barata said that his company supported Villaran at her request, according to testimony he reportedly gave prosecutors in Brazil.
"We made the decision to support her in this process," Barata told the IDL Reporters portal, explaining that the firm had a contract with the municipality of Lima for an urban concession.
"We had a concern that the exit (of Villaran) would generate some difficulty with our contract," Barata told Brazilian prosecutors, according to the portal.
"Then we received the call from the same mayor asking for that contribution. She affirmed the need and importance of continuity," he reportedly said.
Valdemir Garreta, of another Brazilian firm, FX, told prosecutors that he received $3 million to advise Villaran, $2 million of which came from Odebrecht, El Comercio newspaper reported on Wednesday. Villaran denied to IDL that she received any money from Odebrecht for the campaign.
"The declaration Barata made before the Brazilian authorities is false," she said. Villaran emerged victorious in the recall referendum but lost her bid for re-election in 2014.
Odebrecht has admitted to paying $29 million in bribes for public works contracts in Peru. Two former Peruvian presidents, Alejandro Toledo and Ollanta Humala, already face charges for allegedly taking kickbacks from the Brazilian firm.
The scandal has ensnared politicians in several other countries including Ecuador, Mexico, Panama and Venezuela.
Under investigation by the US Justice Department, Odebrecht agreed in December last year to pay a record $3.5 billion fine after admitting to paying $788 million in bribes across 12 countries to secure contracts.
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