On Monday, one man was hacked to death and 17 injured, as rival gangs with machetes and knives fought in Dili.
Eugino Goncalves, 27, died after having his ears slashed off and tongue cut out, his sister Maria said.
Two of the injured were in a critical condition.
Foreign peacekeepers were deployed to restore order.
The crisis, which has left 37 people dead and driven 55,000 from their homes, began when Mari Alkatiri, the prime minister, fired a third of the armed forces.
The move led to gun battles between police and army factions that spilled into gang warfare, looting and arson, and toppled the government in June.
Calm largely returned with the arrival of more than 2,500 foreign peacekeepers and the installation of a new government, but there have been isolated cases of street violence in recent months.
The peacekeeping force is supposed to be scaled down in the coming weeks.