(Updates after market close, adds denial from Grana to sixth graph)
LIMA, Feb 24 (Reuters) - Grana y Montero's shares closed down about 33 percent on Friday after a local magazine reported that the Peruvian construction group knew about $20 million in bribes paid to a former president by its partner, scandal-tainted Brazilian firm Odebrecht SA.
Hildebrandt en sus trece said the former head of Odebrecht Peru, Jorge Barata, told prosecutors that the firm's junior partners on a highway project were aware of an agreement to bribe former President Alejandro Toledo in exchange for help securing the contracts.
Grana and two other local companies helped Odebrecht build two sections of a road from the Peruvian Amazon to Brazil. Odebrecht is embroiled in a massive corruption scandal stretching across a dozen countries.
"The rest of the companies did know, not the details, but they did know there was an agreement," the Hildebrandt report quotes Barata as telling the attorney general's office. "They knew we made the payments and knew they would have to assume their part."
Reuters could not immediately confirm the authenticity of published documents that Hildebrandt said represented Barata's official testimony.
Grana denied knowing about any bribes. "We reiterate our willingness to continue collaborating with the investigations on this case, with the greatest interest in knowing the truth," the company said in a statement.
If Grana is implicated in bribes, the company could see its role as one of the country's biggest construction group's shrink.
Peruvian President Pedro Pablo Kuczynski has banned any company involved in graft from bidding on future public work projects and recently passed a law that would let the government rescind active contracts if projects by those companies are delayed.
Peruvian prosecutors have previously cited Barata's testimony as key in the decision to request the preventive arrest of Toledo, who led the Andean nation from 2001 to 2006.
Toledo, last believed to be in the United States, has denied any wrongdoing and has refused to turn himself in while his lawyer files appeals.
Peru's attorney general's office declined to comment.
Barata, who has agreed to testify in an influence peddling and money laundering case against Toledo, did not immediately respond to requests for comment.
Reporting by Mitra Taj, Ursula Scollo and Teresa Cespedes; Editing by Paul Simao and Lisa Shumaker