Nearly 300 inmates have died so far this year in the country's prisons, and September's gang-related violence was the worst in Ecuador's history.
Some 119 inmates lost their lives
during a riot in the Litoral Penitentiary on 28 September.
The latest fighting at the prison in Guayaquil, Guayas province, has also left 25 people injured and follows a smaller armed clash earlier this month in which three inmates were shot dead.
There were reports of further violence at the prison later on Saturday and soldiers were deployed as reinforcements, securing the outside of the facility in armoured vehicles.
Authorities said the violence started as a territorial dispute between rival groups after a gang leader was released early.
"As this section of the prison was without a ringleader, other gangs tried to... enter to carry out a total massacre," the governor of Guayas province, Pablo Arosemena, told reporters.
On 28 September, inmates from one wing of the prison crawled through a hole to gain access to a different wing, where they attacked rival gang members. Hundreds of officers and army soldiers were deployed to regain control of the complex.
The deadly fight, which saw some inmates decapitated, drew attention to the growing influence in Ecuador of transnational crime gangs such as the Mexico-based Sinaloa and Jalisco New Generation cartels.
Ecuador's prisons are currently accommodating about 9,000 more prisoners than they were designed to hold, officials say. The Litoral Penitentiary was designed for 5,300 inmates but currently holds 8,500.