Fighting between rival gangs in a prison in northern Brazil has reportedly left at least 10 inmates dead, three of them beheaded, in the latest in a series of massacres in the country's jails.

News website Folha de Sao Paulo said the afternoon riot broke out at the Alcacuz Penitentiary in Rio Grande do Norte state after criminal factions clashed and some cell blocks were invaded by rivals.

Zemilton Silva, co-ordinator of the prison system, said "we could see the heads ripped off" three inmates.

Police have surrounded the prison and blocked the exits, but were waiting until daybreak to enter because the inmates were out of their cells and armed.

The last rebellion in Alcacuz prison was in November 2015, when a tunnel was discovered in one pavilion.

The jail should house 620 inmates but has 1,083.

The recent string of Brazilian prison violence began on Jan 1 and 2, when 56 inmates were killed in the northern state of Amazonas.

Authorities said the Family of the North gang targeted members of Brazil's most powerful criminal gang, First Command, in a clash over control of drug-trafficking routes in northern states.

Many of the dead were beheaded and dismembered.

On January 6, in the neighbouring state of Roraima, 33 prisoners were killed, many with their hearts and intestines ripped out.

Experts say First Command, known by the Portuguese acronym PCC, is exploiting overcrowding and squalid conditions in the Brazil's jails to expand its reach across the national prison system.

The gang runs drug-trafficking operations both inside and outside prisons even though many of its leaders are in maximum security jails in Sao Paulo state.