Mari Alkatiri, the prime minister, has described the violence as an attempted coup and speculation has grown that the government could be near collapse.
The government has asked 1,300 Australian troops to help quell the violence, but despite their presence the fighting has continued.
Fires raged across Dili and about 800 people broke into a World Food Programme warehouse in the capital and looted supplies on Monday, witnesses said.
John Howard, the Australian prime minister, said it was up to the people of East Timor to solve the problems, but Australia would offer help and advice.
"In the end, if it is to be an independent country, East Timor has got to run itself," Howard said on Monday.
"I think the situation will get worse. I am ready to leave the country with just the shirt on my back"
Aquilino Soares Torres
Brendan Nelson, the Australian defence minister, said troops were frustrated by rules of engagement that allowed them to do little more than disarm the gangs.
"Our rules of engagement don't extend to applying extreme force to people doing that sort of thing [gang violence]," said Nelson.
Twenty-seven people have been killed in disturbances that began in March as a protest over pay by about 600 disgruntled soldiers.
They threatened to launch a guerrilla war, and the conflict has widened to include the general population, with a split between the east and west of the country.
Australian troops have been
unable to end the violence
About 27,000 East Timorese have sought refuge at shelters, according to the UN.
Aquilino Soares Torres, 34, fled to the airport with his family and said foreign troops were failing to end the conflict.
"The don't move into the neighbourhoods where the violence is taking place," he said, holding a baby in one arm.
"I think the situation will get worse. I am ready to leave the country with just the shirt on my back."
The UN has evacuated its 300 staff from East Timor to Australia. China has said it will send a charter plane to evacuate its nationals.