"We have no evidence at all that any of the violence here in recent times has been co-ordinated by anybody in Indonesia, or that there has been any Indonesian involvement in it," Downer said on Saturday.
More than 100,000 people have
been displaced by the clashes
"Indonesia doesn't want to destabilise East Timor and I think East Timor can do without [such] canards."
Alkatiri, who has been blamed by many East Timorese for sparking the violence with his sacking of 600 protesting soldiers, said on Friday that some of the violence had been carried out by pro-Indonesian militias.
Also on Saturday, the UN warned that the violence that has paralysed much of Dili could spill over into camps set up to house about 100,000 people displaced by recent fighting.
"People are living in a desperate situation, cheek to jowl," said Gregory Garras, head of the UN refugee agency's emergency team in East Timor.
"People are living in a desperate situation, cheek to jowl. There's no privacy, it's hot and there is insufficient water"
Gregory Garras, head of UN emergency team in East Timor
"There's no privacy, it's hot, there's insufficient water. The conditions are absolutely untenable."
Fighting erupted in the country two weeks ago. Violence spread as rival gangs rampaged across the country, killing at least 20 people and forcing tens of thousands to leave their homes.
Australia last led troops into East Timor in 1999 to restore law and order after violence by militia groups, supported by elements of the Indonesian military, broke out following a vote to break free of Indonesian rule.