Olmert, who was premier between 2006-2009, was convicted of graft and entered prison in February 2016.
The president noted that the grounds for the request -- including Olmert's contributions to Israel over the years -- were known to the court when it sentenced the former prime minister.
Rivlin also said in a statement that Olmert was due to face a parole committee, which would discuss his request to have his sentence shortened by a third.
Olmert is Israel's first former premier to serve jail time.
He resigned as prime minister in September 2008 after police recommended he be indicted for graft, but remained in office until March 2009, when Likud leader Benjamin Netanyahu was sworn in to the post, which he has held ever since.
Olmert won international acclaim for relaunching peace efforts with the Palestinians at the Annapolis conference in the United States in 2007, but they failed to bear fruit and the corruption charges against him have come to define his legacy.
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