They also released a list of 34 names of opposition chiefs, civil society leaders and journalists - now in exile - they want to face trial for their alleged role in the May 2015 coup bid.
The appeal comes after a court in January jailed 21 men for their role in the coup, sentencing four ex-generals to life, nine others for 30 years, and eight soldiers to five years.
Prosecutors, who said in a statement that they were "not satisfied with the judgement of the trial judge", said they should all be jailed for life, and that the seven acquitted should face a re-trial.
Coup leader, ex-general Godefroid Nyombare, is on the run. The former intelligence chief has been named as leader of the Forebu rebels.
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The rebels formed the force "to protect the population" and uphold the Arusha Agreement that paved the way to the end of the 1993-2006 civil war - but which they say Nkurunziza violated by running for, and winning, a third term in power.
Since then, clashes between loyalists and the opposition have turned increasingly violent, with hundreds killed and at least 230,000 fleeing the country.
Instead, the AU is to send envoys for more talks, although previous negotiations have achieved little, if anything.