"President Reuven Rivlin today took the decision to deny the request for pardon filed by Elor Azaria," it said in an English-language statement, exactly one month after the jailed soldier submitted his request.
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On July 30, a military court turned down Azaria's appeal against his conviction for manslaughter and upheld an 18-month prison sentence, which he began serving on August 9.
In September, Israel's Chief of Staff General Gadi Eisenkot reduced the term by four months.
He will therefore complete his term in October 2018 unless the routine parole board considers him for earlier release when it reviews his case early next year.
Rights group Amnesty International has said Azaria's sentence does "not reflect the gravity of the offence".
The UN human rights office said it was an "unacceptable" punishment for "an apparent extra-judicial killing".
However, both Prime Minister Benjamin Netanyahu and Defence Minister Avigdor Lieberman have supported a full pardon.
The written reply to the pardon application, quoted in Sunday's statement, says that Rivlin noted Eisenkot's clemency and the court's "lenient" sentence.
"The President learned that in passing sentence, the military court took into account the circumstances raised by you... as consideration of leniency, and he noted it took them into account in passing a lighter sentence," it said.
Lieberman 'saddened'
Lieberman said in response that he respected Rivlin but was saddened at his ruling.
"I regret his decision to reject the request for a pardon of the soldier Elor Azaria," he said in a statement.
"President Rivlin had an opportunity to put an end to this affair, which has shaken Israeli society," he added.
Lieberman said he believed it would have been in the public interest "to weigh the need to heal the rifts in society" opened by the case.
Last year's shooting deeply divided Israel and led to an extraordinary rift between right-wing politicians who wanted to see Azaria released and top military brass, who harshly condemned his actions.
Rivlin's decision stressed the potential damage done by the incident to the Israeli military's moral code.
"An additional lightening of your sentence would damage the Israel Defence Forces and the state of Israel," it said, adding that Azaria was expected to come before the parole board "in approximately three months" where his release under licence would be considered.
The March 2016 shooting in the occupied West Bank city of Hebron was caught on video by a human rights group and spread widely online.
It showed Abdul Fatah al-Sharif, 21, lying wounded on the ground, shot along with another Palestinian after stabbing and wounding a soldier, according to the army.
Some 11 minutes after the initial shooting, Azaria, a sergeant and military medic at the time, shot him in the head without any apparent provocation.
He said he had feared Sharif was wearing an explosive belt and could blow himself up -- a claim judges rejected.
Azaria completed his mandatory three-year military service on July 20.
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