At least two people have been reported killed in the latest clashes overnight on Wednesday. Their bodies were found in an embassy area of the capital, Dili.
The latest deaths bring the number of killed in five days of fighting to at least six.
More than 50 people have been injured, and dozens of homes and businesses destroyed.
Australian-led international peacekeepers have been patrolling the streets of the city and the area around the airport in an effort to restore calm after almost a week of escalating violence.
On Tuesday, officials closed Dili’s small international airport saying they could not guarantee security for passengers there.
Jose Ramos Horta, the Timorese prime minister, has blamed the violence on gangs of "common criminals, who deliberately targeted defenceless citizens".
Horta, a winner of the Nobel Peace Prize, was an instrumental figure in East Timor’s long and bloody struggle for independence from Indonesia.
Speaking from Rome, where he is on an official visit, he said he had been in contact with Mari Alkatiri, the former prime minister who resigned in June amid growing criticism from inside and outside East Timor.
In April this year fighting between rival members of the country’s security forces forced tens of thousands of people to flee their homes.
Two months of street battles left more than 30 people dead before an Australian-led peacekeeping force arrived to try to restore order.
A United Nations report into the violence released this month put much of the blame for that fighting on the former Alkatiri government.
The report accused former ministers and members of the security forces of allowing weapons to fall into civilian hands, and said Alkatiri himself should be investigated for any criminal responsibility.
The release of the UN report is thought to have sparked the latest round of fighting.
The resurgence of gang violence in East Timor has led to criticism from some parts that the UN, which oversaw the country’s transition to independence in 2001, largely abandoned the country to run itself before a civilian infrastructure had fully developed.