In their appeal, prosecutors noted that prior to sentencing they had asked for three to five years imprisonment in the case that has deeply divided Israeli society.
The appeal, a copy of which was provided to AFP, also noted that the three-judge panel had passed the sentence last month by a two to one majority, with the dissenting justice recommending 30 months.
"The prosecution argues that the punishment imposed on the respondent is excessively lenient and is not consistent with the level of punishment which is acceptable and appropriate to the respondent's deeds," it said.
The prosecution's appeal came after Azaria's lawyer filed an appeal against his client's conviction for manslaughter.
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He was due to begin his sentence on March 5, but a military appeals court accepted the defence's request to delay the sentence until judgement of his appeal.
He is to be confined to base in the meantime.
Defence attorney Yoram Sheftel said on March 2 that he would be ready to begin the appeal within six weeks.
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.
Azaria then shot him in the head without any apparent provocation.
Azaria said he feared Sharif was wearing an explosive belt and could blow himself up, a claim judges rejected.
His sentence, with another 18 months suspended, was condemned as too stern by rightwing politicians and labelled too lenient by Palestinians and rights groups.