Rivlin's office said in a statement that the request to then president Yitzhak Ben-Zvi would be presented at a ceremony at Rivlin's official Jerusalem residence to mark International Holocaust Remembrance Day.
In the petition, written after he was brought to Israel in 1960, then tried, convicted and sentenced to death the following year, Eichmann says that the Israeli court overstated his role in organising the logistics of Hitler's "Final Solution" which involved the extermination of six million Jews.
"There is a need to draw a line between the leaders responsible and the people like me forced to serve as mere instruments in the hands of the leaders," Rivlin's office quotes the letter as saying.
"I was not a responsible leader, and as such do not feel myself guilty," he adds.
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"I am not able to recognise the court's ruling as just, and I ask, Your Honour Mr President, to exercise your right to grant pardons, and order that the death penalty not be carried out."
The letter was signed and dated: "Adolf Eichmann Jerusalem, May 29, 1962."
He was hanged on May 31.
Eichmann escaped from a prisoner-of-war camp after World War II and fled to Argentina in 1950, where he lived under a pseudonym until he was snatched by Mossad agents in Buenos Aires in May 1960 and smuggled to Israel.
Other documents to be presented at Wednesday's commemoration, in the presence of Holocaust survivors, include requests for clemency from Eichmann's wife Vera and his five brothers, along with Ben-Zvi's letter to his justice minister rejecting the appeals.
Also in the collection, recently digitised by the presidential archives, are a transcript of Eichmann's defence counsel's Supreme Court appeal, the handwritten opinion of Justice Minister Dov Yosef, and a note by prosecutor Gideon Hausner for his opening address.