Prosecutors in East Timor have issued arrest warrants for 18 suspects believed to be involved in Monday's attacks on the nation's top leaders.
Australia is reinforcing its peacekeeping force in East Timor
President Jose Ramos-Horta was shot three times, while PM Xanana Gusmao escaped unhurt from a separate attack.
Meanwhile, parliament has approved plans to extend for 10 days a state of emergency imposed after the attacks.
Australian troops are continuing to arrive in the country, reinforcing international peacekeepers.
The UN force has been in East Timor since a wave of street violence in mid-2006.
A group of rebel soldiers with grievances that date back to that unrest are thought to have been behind Monday's attacks.
Prosecutor-General Longinhos Monteiro issued the arrest warrants, a move which the BBC's Jonathan Head in Dili says gives international peacekeepers a clear mandate to go after the rebels.
No arrests have been made so far. Renegade soldier Alfredo Reinado was killed in the attack, along with another rebel.
The situation in Dili remained calm, despite fears that the attacks would trigger further unrest.
Peacekeepers and East Timorese troops have been maintaining a heavy presence and a night-time curfew has been in place.
"This emergency status is not intended to hinder people's activities but to allow the normalisation of the situation," said Mr Gusmao, who proposed the 10-day extension of the emergency.
"I call on the people to remain calm and abide by government rules."
Every vehicle leaving the capital is being thoroughly searched by the police and weapons as small as pocket knives are being confiscated.
They are also forcing all cars to remove tinting from their windows.
By far the heaviest security was seen at the town's hospital, where armed Portuguese riot police surrounded the convoy of ambulances carrying Reinado's body.
Weeping mourners were given a glimpse of the corpse at his house, ahead of his burial on Thursday.
So far there has been no reaction by his followers to the deaths.
In Darwin, Australia, doctors carried out a third operation on Mr Ramos-Horta, who was shot in the chest and stomach in the pre-dawn attack outside his Dili residence.
"I am pleased to report that the president is doing very well," said Royal Darwin Hospital surgeon Professor Phil Carson.
"Everything is looking very, very good."
He was expected to remain in an induced coma for several days, doctors said.
The twin attacks have shocked residents in East Timor, one of the world's newest and poorest nations.
Reinado, a former military officer, had been on the run with a group of followers since the wave of violence that swept through East Timor in mid-2006.
He was accused of being involved in several shooting incidents during the violence and charged with murder.
As many as 30 rebels with weapons remain at large in the mountains behind Dili, together with several hundred other so-called petitioners who supported his rebellion.
But our correspondent says despite the shock caused by the attacks and the continued uncertainty over Mr Ramos-Horta's condition, some in the government hope this incident may prove an opportunity to discredit the romantic image of armed insurrection still left over from the long war against Indonesian rule.