SÃO PAULO—More than 100 escaped prisoners in Brazil were on the run Tuesday after breaking out during a bloody prison riot that left 60 inmates dead and sparked criticism of chronic overcrowding in the country’s jails.

As warring drug gangs in two prisons in the Amazonian city of Manaus stabbed, decapitated and dismembered fellow inmates during a 17-hour riot that ended Monday, 184 prisoners escaped. Many of them scrambled away through the dense rain forest surrounding the city on the Amazon river, according to police and...