MEDELLÍN, Colombia — President Nicolás Maduro of Venezuela received at least $35 million dollars in bribes from a Brazilian construction company in 2013, according to a video posted on a blog run by the country’s former attorney general, who fled the country in August.

In the video, a man identified as Euzenando Prazeres de Azevedo, who managed the Venezuelan operations of the company, Odebrecht, said he was “asked for a large sum” by a representative of Mr. Maduro when he was running for the presidency in 2013.

“He asked for 50, and I accepted to pay him 35 million,” Mr. Azevedo said in the video, published on the blog of Luisa Ortega, who was ousted as attorney general after repeated clashes with the president as he tightened his grip on power and jailed opponents.

The recording was said to have been made by Brazilian prosecutors last December.

The president’s ’s office made no immediate comment Thursday about the accusation, and state television did not mention it.

Vladimir Aras, a senior Brazilian prosecutor who until recently led the attorney general’s international cooperation office, said that the recording was authentic and that it had been part of Ms. Ortega’s investigation of Odebrecht, which extended to the president’s office.

“Independent prosecutors aren’t helpful to dictatorships,” he said of Ms. Ortega.

The recording adds Mr. Maduro to a lengthening list of Latin American leaders who have been caught up in the Odebrecht bribery scandal. The construction giant was the go-to company in the Americas and beyond for everything from highways to tunnels and bridges. Then last year it admitted to running an enormous bribery racket through a secret department that paid nearly $800 million to high-ranking officials in exchange for contracts.

The revelation sent shock waves through several South American capitals.

Earlier this month, a judge in Ecuador ordered the arrest of that country’s vice president, Jorge Glas, as part of a bribery investigation and also ordered his assets frozen. Ollanta Humala, a former Peruvian president, was arrested over allegations that he had taken at least $3 million in illegal campaign contributions. Another former Peruvian president, Alejandro Toledo, remains at large on a warrant that accuses him of receiving millions in bribes from Odebrecht.

All three men have denied wrongdoing.

Last year, Marcelo Odebrecht, the company’s former chief executive, was sentenced by a court in Brazil to 19 years in prison after being convicted on charges of corruption and money laundering.

The accusation against Mr. Maduro is perhaps the most explosive yet, both for the amount of money said to be involved and the fact that he still leads the country.

On the tape, Mr. Azevedo describes the run-up to 2013 election when the company had many projects in the works in Venezuela, but their patron, President Hugo Chávez, was terminally ill with cancer.

Shortly after Mr. Chávez died, Mr. Azevedo says, he was approached by Américo Mata, who he says was the head of Venezuela’s rural development agency. Mr. Azevedo describes Mr. Mata as a “representative of Mr. Nicolás Maduro,” who at the time was the vice president and Mr. Chávez’s handpicked successor.

“We met at various times at a Venezuelan delicatessen, and one day he asked for a contribution,” Mr. Azevedo said. “He knew about our business and the size of our operation.”

On the recording, Mr. Azevedo says he gave $50 million, but then corrects himself to say the amount was actually $35 million.

The 2013 election became a contest between Mr. Maduro and Henrique Capriles, a state governor. During the campaign, Mr. Maduro was criticized for using state giveaways to entice Venezuelans to vote for him, a practice that Mr. Chávez was also known for.

“We accepted to pay, the funds were made available for him during the campaign, and President Maduro won the elections by a narrow margin,” Mr. Azevedo says on the recording. The difference was roughly 1.5 percent.

In July, an investigative report published by the Brazilian newspaper O Globo said Mr. Azevedo had made payoffs both to Mr. Maduro and Mr. Capriles. Mr. Capriles has denied the allegation, saying he had “no relation” with Odebrecht.

The leaked tape puts Ms. Ortega, the ousted attorney general, back into the spotlight as she wages a public feud with her former boss.

Ms. Ortega, a longtime member of Mr. Maduro’s leftist ruling party, became one of the president’s most vocal critics this year. She challenged an attempt by Mr. Maduro’s allies in the Supreme Court to dissolve the country’s legislature, criticized his crackdown against protesters and said an attempt to establish a body to rewrite the Constitution was illegal.

Mr. Maduro’s allies eventually had her removed from her post, leading to a dramatic scene in which she fled the attorney general’s compound on the back of a motorbike.

Shortly afterward, she departed the country. She has spent much of her time in neighboring Colombia vowing to release incriminating information against the president.