East Timor's former Prime Minister Mari Alkatiri has called on current Prime Minister Xanana Gusmao to resign, amid claims he orchestrated deadly unrest that erupted in 2006.

Alkatiri resigned as prime minister in June that year after a request from then President Gusmao, based on allegations that Alkatiri and several of his ministers gave instructions to arm civilian militia during the crisis.

His government had earlier sacked more than a third of the country's defence force, sparking factional violence that left 37 people dead and drove 100,000 from their homes.

Many of the sacked soldiers joined the rebellious former military police chief Alfredo Reinado, who last week alleged Gusmao was the "mastermind" who had fomented the unrest.

"I think that it is time for Xanana to resign from his post because he has established a precedent in 2006 based on allegations without fact," Alkatiri said on Sunday.

Alkatiri said the people of East Timor were waiting to find out the truth behind the crisis. Gusmao should resign and submit to justice, he said. "Nobody in this country is untouchable," Alkatiri said.

He said a task force set up to investigate the 2006 crisis was a sham and would never return and adverse finding against Gusmao. President Jose Ramos-Horta should also be pushing for Gusmao's resignation, Alkatiri said.

"Ramos-Horta, as foreign minister, was very supportive of Xanana to force me to resign. Now he is president of the republic and he has to do the same."

Local media last week reported that Gusmao was refusing to respond Reinado's claims, saying he did not want to engage in a "war of words". (AAP)