On how long Australian troops would stay in the fledgling nation, Rudd said: "So long as they are invited here by the government of East Timor."
Australia, which lies a short flight south of East Timor, is the single largest contributor of foreign forces in East Timor with more than 1,000 army and police on the ground.
Arrest warrants issued
Meanwhile, East Timor prosecutors said on Friday they issued arrest warrants for 12 suspects in the attacks on the country's top two leaders.
Longuinhos Monteiro, the attorney general, told reporters in Dili that 12 warrants were handed over to police and that five more may follow soon.
The names of the suspects were not immediately released. Police are investigating the circumstances behind the strikes.
It has yet to be established whether they were assassination attempts or part of a failed coup.
There has also been speculation that rebel leader Alfredo Reinado intended to kidnap Jose Ramos-Horta, the president and Nobel Peace Prize winner.
The rebels shot and critically wounded Ramos-Horta outside his home on Monday. His guards killed Reinado during the attack.
An hour later, gunmen opened fired on Xanana Gusmao, the prime minister, but he escaped unhurt.
Ramos-Horta - who won the 1996 Nobel Peace for his non-violent campaign against the East Timor's occupation by Indonesia - is being treated for gunshot wounds to the upper body in a hospital in the Australian city of Darwin.
Doctors have performed several operations on the 58-year-old, but expect him to make a full recovery.