Australia is likely to face pressure not to weaken its peacekeeping commitment to East Timor when the trilateral talks begin in Dili.
Canberra is preparing to scale down its troop commitment to the nation and Mr Downer said he would encourage East Timor's leaders not to rely on international forces.
The United Nations has agreed to the deployment of more than 1,600 international police to East Timor, and Mr Downer said less Australian troops would be required.
"The East Timorese have to accept responsibility for their own affairs and work to solve their own problems, not expect us and the United Nations to fix up all their problems," he said.
Mr Foreign Minister Alexander Downer arrived in the capital last night amid concern about fresh violence and a mass jail break which is threatening further instability in the fledgling nation.
Rebel leader Alfredo Reinado and 56 other inmates walked out of Dili's Becora prison last Wednesday afternoon.
None of the men have been recaptured, forcing Jakarta to step up security along the border with Indonesian West Timor.
Mr Horta has said Australia must accept some of the blame for the jail break because his government asked repeatedly for extra patrols around the jail.
In addition, five people suffered gunshot wounds in a camp in Dili on Friday and a sixth was wounded in a machete attack.
'Troops should remain': Rudd
Opposition foreign affairs spokesman Kevin Rudd says Australia must keep substantial numbers of Australian troops on the ground in East Timor until elections can be held early next year.
Mr Rudd says Australia should not repeat its mistake of 2005 when it withdrew soldiers before the security was established.
"Mr Downer is saying that East Timor's security and their own affairs is up to the East Timorese themselves. You can't have this both ways: a government which says East Timor is its proudest achievement and then trying to walk away sideways from any responsibility," Mr Rudd said.
He said the government should conduct a review of the failings of Australian training programs for the East Timorese police and armed forces prior to the collapse of security earlier this year.
UN Commissioner
Meanwhile the UN police commissioner for East Timor, Antero Lopes, has predicted that last week’s prison escapees will be returned soon.
"I believe that soon we will start assisting some of those escapees returning to the prison or eventually being captured," Mr Lopes told ABC Radio.
Mr Lopes said the wider East Timorese community would not welcome the escapees.
"Most of them (the escapees) are convicted criminals and they are not welcome in the community," he said.
Major Reinado has issued a statement from his hideout but Mr Lopes said investigators did not know where the interview took place.
"I don't have any information that would make me conclude that he (Major Reinado) would be a threat to the government. I believe he's making statements about what he believes is the political situation, but those are his own views and I would not comment on the political aspect of it," Mr Lopes said.