Lee Jae-Yong, the de-facto head of Samsung Electronics, was found guilty last week of bribery, perjury and other charges related to payments made by Samsung to ousted president Park Geun-Hye's secret confidante Choi Soon-Sil.
Four other top Samsung executives were also convicted, with two jailed for up to four years, and the other pair given suspended terms.
The prosecutors appealed part of the verdict that found Lee innocent of some of the bribery charges and said the punishment meted out to the five accused was too mild, Yonhap news agency said.
A day earlier, lawyers for Lee filed their own appeal against the conviction, claiming he is innocent of all charges.
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In total 8.9 billion won (USD 7.9 million) was paid in bribes in return for favours including government support for Lee's hereditary succession at the group after his father was left bedridden by a heart attack in 2014, the court found.
But while the economy is still growing, frustrations have mounted over inequality and the demonstrators who mounted giant candlelit protests against Park last year also targeted Lee and other chaebol chiefs.