It comes amid what appears to be a crackdown against those suspected of involvement in the plot.
The BBC has seen evidence of retaliatory attacks, after a hospital where soldiers involved in the coup were being treated was attacked.
The alleged coup ringleader, Godefroid Niyombare, is still on the run.
President Nkurunziza on Saturday thanked the army for thwarting the coup and appealed for calm, although protests have continued in the capital Bujumbura.
Those who appeared in court in Bujumbura included former defence minister General Cyrille Ndayirukiye and police commissioners Zenon Ndabaneze and Hermenegilde Nimenya, said lawyer Anatole Miburo, quoted by AFP news agency.
Mr Miburo said they had been accused of attempting to overthrow the state.
"They were seriously beaten, in particular General Ndayirukiye," he said.
Relatives of two of the accused told the Reuters news agency that the suspects had visible injuries and that one had lost hearing in one ear due to a beating in the cells.
The BBC's East Africa correspondent Karen Allen says it is alleged that three soldiers were dragged from a hospital in Bujumbura during a police raid.
A fourth died of his injuries but doctors were unable to confirm whether these were wounds sustained during the police attack or injuries for which he was originally admitted to hospital.
President Nkurunziza was in Tanzania on Wednesday when military leaders moved against his bid for a third term.
He returned home on Friday, initially travelling to his northern hometown of Ngozi, before continuing to Bujumbura.
Security remains tight in the capital, where private radio stations are still closed. Soldiers and police have been patrolling the streets looking for anyone involved in the coup.
The president has moved quickly to reassert his authority, and there is nervousness inside and outside Burundi that old wounds from the civil war which ended in 2005 could be re-opened, our correspondent says.
10.4m population
50 years - life expectancy for a man
2nd poorest country in the world
85% are Hutu, 14% Tutsi
300,000 died in civil war
The unrest in Burundi started on 26 April, with protests sparked by Mr Nkurunziza's announcement a day earlier that he would run for re-election in June.
Opponents said the bid contravened the constitution, which states a president can only be elected to two terms.
The president argued that he was entitled to a third term because he was first appointed to the role by parliament in 2005, rather than elected.
Since then, at least 25 people have been killed and more than 105,000 people have fled the country.
Eighteen people have appeared in court in Burundi accused of helping to organise last week's failed coup against President Pierre Nkurunziza.