Toledo, who has earned economics degrees from Stanford University, has denied wrongdoing and has not been charged or convicted of any crimes.
On Friday, Peru asked American authorities for help in detaining and extraditing Toledo after learning he was in San Francisco and meant to go to Israel, where his wife holds dual-citizenship.
Odebrecht agreed to pay out $3.5 billion after bribing corrupt government officials in the U.S., Brazil and Switzerland through shell companies.
He said Toledo met the head of Odebrecht Peru, Jorge Barata, in a luxury hotel in Rio de Janeiro in 2004 and promised to help the firm win two highway contracts in exchange for $35 million.
Alejandro Toledo is alleged to have taken a Dollars $20 million bribe for awarding a lucrative contract to Odebrecht (La Mula).
Peruvian Judge Richard Concepcion on Thursday ordered the arrest [press release, in Spanish] of former president Alejandro Toledo for his alleged involvement with a bribery scandal involving the Brazilian construction company Odebrecht SA [official website].
If captured, Toledo will be detained for up to 18 months as prosecutors prepare charges against him.
But he has struggled to explain where the money came from.
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According to AFP he originally said it was a loan from his mother-in-law that came from compensation she received as a Holocaust survivor.
Prosecutors say that the bribes were paid to Toledo through a proxy, Josef Maiman, a Peruvian-Israeli businessman and friend of the former president.
"Lies just flow out of him", he said, adding a message for his former boss: "If it turns out you're guilty and you go to jail, then rot in there".
"Toledo will be allowed in Israel only when his affairs in Peru are settled", foreign ministry spokesman Emmanuel Nahshon said in a statement earlier in the day.
"US authorities have been asked to cooperate in detaining and deporting him", it said.
The dispute threatens to strain relations between the United States and one of its traditional allies in South America.
Interpol issued a red alert notice to 190 member countries to search for and capture Toledo, Kuczynski's Cabinet said on Friday.