The president said he had done nothing wrong. He said the leaked recordings had been edited in a “selectively biased way that gave the impression that the government was offering public works in exchange of votes.”
Analysts said that the resignation did not bode well for Latin America, where Peru’s economic stability has contrasted with growing political turmoil.
“This is not a good precedent for Peru or for the region, that an opposition could essentially force out the president this way,” said Michael Shifter, the president of the Inter-American Dialogue, a policy group in Washington. “Peru has been a puzzle and a paradox — it’s been such an economic performer, but you have such weak political institutions.”
It is still unclear whether Congress will decide to accept Mr. Kuczynski’s resignation or choose to impeach him anyway. This happened to Mr. Fujimori, who resigned in 2000 after fleeing to Japan. Congress rejected his resignation and impeached him instead. Years later he faced trial in Peru, and the country’s Supreme Court sentenced him to 25 years in prison on human rights violations.
Lawmakers on Wednesday expressed anger that Mr. Kuczynski had not apologized.
“We hoped that his resignation letter would have at least some self-criticism of the mistakes and crimes he may have committed,” said Marco Arana, who leads the leftist Broad Front. “Instead, he just plays the victim in his letter and doesn’t admit anything.”
Mr. Kuczynski was set to be replaced by his vice president, Martín Vizcarra, who is also serving now as ambassador to Canada. Mr. Vizcarra himself was once forced by Congress to resign when he served in Mr. Kuczynski’s cabinet, although opposition lawmakers have in recent weeks spoken highly of him. Mr. Vizcarra has not spoken publicly about the controversy, and it was not clear on Wednesday whether he was even in Peru.
“This was a government that carved its tomb from Day 1,” said Eduardo Dargent, a political scientist at the Pontifical Catholic University of Peru. “Looking forward, it’s very unclear what will happen.”
Mr. Kuczynski, a former Wall Street banker and World Bank economist who was educated at Oxford and Princeton, campaigned in 2016 on a liberal platform that promised economic growth and “social revolution.” He narrowly beat Keiko Fujimori, the daughter of the former leader.
Last year, Congress accused Mr. Kuczynski of “permanent moral incapacity” for profiting from contracts with Odebrecht, the Brazilian corporate giant now troubled by scandal, during a period in the early 2000s when he served as a cabinet member. Mr. Kuczynski said he was merely a shareholder in a company that profited from Odebrecht deals.
Congress’s impeachment effort had been enthusiastically supported by the Popular Force, the party led by Ms. Fujimori.
But Mr. Kuczynski avoided removal in December, thanks to Ms. Fujimori’s brother Kenji Fujimori, a congressman who split with his sister and carried enough lawmakers to his side to save the president. Two days after the failed ouster, Mr. Kuczynski pardoned Alberto Fujimori on medical grounds.
The apparent deal allowed Mr. Kuczynski to save his political career in the short term, but it soon created a much larger problem, analysts say. By pardoning the elder Mr. Fujimori, after his conviction as a human rights abuser, the president alienated supporters who had remained with him.
“It was his willingness to do these dirty deals to stay in power that was key” to his loss of support, said Jo-Marie Burt, a political scientist who studies Latin America at George Mason University in Virginia. “He betrayed many of the promises he said he would uphold.”
The sentiment was echoed widely in Peru on Wednesday.
“I feel sorry about this, but this is the end that Mr. Kuczynski deserves,” said Pedro Cateriano, a former prime minister who counseled the president during the first impeachment attempt.
The tapes, recorded by an ally of Keiko Fujimori who pretended to be toying with the idea of switching sides, appeared to trace graft to the highest levels of government. They showed Kenji Fujimori, and some people close to him, offering favors and public works projects in exchange for political support.
In one video, Bienvenido Ramírez, a congressman, bragged about all the benefits he had received because of his support of Mr. Kuczynski.
“In less than a week I got the public works that I wanted,” Mr. Ramírez can be heard saying. He also mentioned that a government official had been assigned to help expedite any projects that were of interest to him.
Another government official tried to explain how to earn big rewards while in Congress.
“Imagine, brother, that in a $100 million public works that you receive only 5 percent,” said Freddy Aragón, a government official who was fired Tuesday night. “Brother, you get $5 million without lifting a finger.”
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